Top Banner

of 71

Nonlinear Controls theory

Jul 07, 2018

Download

Documents

D.J.
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
  • 8/18/2019 Nonlinear Controls theory

    1/71

  • 8/18/2019 Nonlinear Controls theory

    2/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    3/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    4/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    5/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    6/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    7/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    8/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    9/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    10/71

  • 8/18/2019 Nonlinear Controls theory

    11/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    12/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    13/71

  • 8/18/2019 Nonlinear Controls theory

    14/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    15/71

  • 8/18/2019 Nonlinear Controls theory

    16/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    17/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    18/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    19/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    20/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/2019 Nonlinear Controls theory

    21/71

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

    catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca

    tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc

    atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat

  • 8/18/