Stability Criterion 2: Lyapunov Stability Theorem
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Example
XTX
murmur
iz 2 2
dVf Vix 2x I 12 2 2
2XC X 12 2 12 Xz 2 27
2 5 4 1 2 4 3 Z X Xz 2 22
Thus Vey D iff x 2 0
Vex 0 for all x f to
Example EERO
Lyapunov stability theorem
O
U xTPx xtPx CAxJpxtxTPcAx xTATpx xTPAX xT AT A x
Let Q CAMPA Then Vex xTQx 7
Time-derivative of Lyapunov function
XTX
murmur
iz 2 2
dVf Vix 2x I 12 2 2
2XC X 12 2 12 Xz 2 27
2 5 4 1 2 4 3 Z X Xz 2 22
Thus Vey D iff x 2 0
Vex 0 for all x f to
Example EERO
Lyapunov stability theorem
O
U xTPx xtPx CAxJpxtxTPcAx xTATpx xTPAX xT AT A x
Let Q CAMPA Then Vex xTQx 7
Time-derivative of Lyapunov function
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