Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —

Page 1 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/1.jpg' width='140' height='200' /> Chapter 4Lyapunov Stability

Page 2 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/2.jpg' width='140' height='200' /> Page 3 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/3.jpg' width='140' height='200' /> Page 4 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/4.jpg' width='140' height='200' /> Page 5 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/5.jpg' width='140' height='200' /> Page 6 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/6.jpg' width='140' height='200' /> Page 7 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/7.jpg' width='140' height='200' /> Page 8 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=8' data-page='8' class='cut-thumb lazyload' alt='Page 8: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/8.jpg' width='140' height='200' /> Page 9 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=9' data-page='9' class='cut-thumb lazyload' alt='Page 9: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/9.jpg' width='140' height='200' /> Page 10 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=10' data-page='10' class='cut-thumb lazyload' alt='Page 10: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/10.jpg' width='140' height='200' /> Page 11 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=11' data-page='11' class='cut-thumb lazyload' alt='Page 11: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/11.jpg' width='140' height='200' /> Page 12 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=12' data-page='12' class='cut-thumb lazyload' alt='Page 12: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/12.jpg' width='140' height='200' /> Page 13 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=13' data-page='13' class='cut-thumb lazyload' alt='Page 13: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/13.jpg' width='140' height='200' /> Page 14 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=14' data-page='14' class='cut-thumb lazyload' alt='Page 14: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/14.jpg' width='140' height='200' /> Page 15 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=15' data-page='15' class='cut-thumb lazyload' alt='Page 15: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/15.jpg' width='140' height='200' /> Page 16 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=16' data-page='16' class='cut-thumb lazyload' alt='Page 16: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/16.jpg' width='140' height='200' /> Page 17 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=17' data-page='17' class='cut-thumb lazyload' alt='Page 17: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/17.jpg' width='140' height='200' /> Page 18 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=18' data-page='18' class='cut-thumb lazyload' alt='Page 18: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/18.jpg' width='140' height='200' /> Example: The Pendulum

Page 19 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=19' data-page='19' class='cut-thumb lazyload' alt='Page 19: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/19.jpg' width='140' height='200' /> Example : The Pendulum(1)

1 2

2 2 12

1 1 2 21 2

1 2 1 2

* *1 2

2

22

sin

0, 1, cos ,

0 10, 0,

0

x xb gx x x

MR Rf f f fg bxx x x R x MR

x x A g bR MR

b gs sMR R

Page 20 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=20' data-page='20' class='cut-thumb lazyload' alt='Page 20: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/20.jpg' width='140' height='200' /> Example: The Pendulum(2)

* *1 2

2

22

*1 1 1 1 2 2

1 2

2 2 12

0 1, 0,

0

,

sin( )

x x A g bR MR

b gs sMR R

z x x x z xz z

b gz z zMR R

Page 21 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=21' data-page='21' class='cut-thumb lazyload' alt='Page 21: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/21.jpg' width='140' height='200' /> Page 22 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=22' data-page='22' class='cut-thumb lazyload' alt='Page 22: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/22.jpg' width='140' height='200' /> Page 23 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=23' data-page='23' class='cut-thumb lazyload' alt='Page 23: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/23.jpg' width='140' height='200' /> Page 24 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=24' data-page='24' class='cut-thumb lazyload' alt='Page 24: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/24.jpg' width='140' height='200' /> Page 25 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=25' data-page='25' class='cut-thumb lazyload' alt='Page 25: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/25.jpg' width='140' height='200' /> Page 26 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=26' data-page='26' class='cut-thumb lazyload' alt='Page 26: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/26.jpg' width='140' height='200' /> Page 27 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=27' data-page='27' class='cut-thumb lazyload' alt='Page 27: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/27.jpg' width='140' height='200' /> Page 28 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=28' data-page='28' class='cut-thumb lazyload' alt='Page 28: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/28.jpg' width='140' height='200' /> Page 29 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=29' data-page='29' class='cut-thumb lazyload' alt='Page 29: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/29.jpg' width='140' height='200' /> Page 30 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=30' data-page='30' class='cut-thumb lazyload' alt='Page 30: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/30.jpg' width='140' height='200' /> Page 31 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=31' data-page='31' class='cut-thumb lazyload' alt='Page 31: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/31.jpg' width='140' height='200' /> Page 32 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=32' data-page='32' class='cut-thumb lazyload' alt='Page 32: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/32.jpg' width='140' height='200' /> Page 33 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=33' data-page='33' class='cut-thumb lazyload' alt='Page 33: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/33.jpg' width='140' height='200' /> Page 34 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=34' data-page='34' class='cut-thumb lazyload' alt='Page 34: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/34.jpg' width='140' height='200' /> Page 35 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=35' data-page='35' class='cut-thumb lazyload' alt='Page 35: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/35.jpg' width='140' height='200' /> Page 36 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=36' data-page='36' class='cut-thumb lazyload' alt='Page 36: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/36.jpg' width='140' height='200' /> Page 37 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=37' data-page='37' class='cut-thumb lazyload' alt='Page 37: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/37.jpg' width='140' height='200' /> Example

Page 38 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=38' data-page='38' class='cut-thumb lazyload' alt='Page 38: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/38.jpg' width='140' height='200' /> Page 39 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=39' data-page='39' class='cut-thumb lazyload' alt='Page 39: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/39.jpg' width='140' height='200' /> Page 40 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=40' data-page='40' class='cut-thumb lazyload' alt='Page 40: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/40.jpg' width='140' height='200' /> Page 41 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=41' data-page='41' class='cut-thumb lazyload' alt='Page 41: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/41.jpg' width='140' height='200' /> Page 42 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=42' data-page='42' class='cut-thumb lazyload' alt='Page 42: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/42.jpg' width='140' height='200' /> Page 43 <img data-url='document/chapter-4-lyapunov-stability-for-stability-is-called-a-lyapunov-function-the.html?page=43' data-page='43' class='cut-thumb lazyload' alt='Page 43: Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021418/5ad5ee947f8b9a6d708d7946/html5/thumbnails/43.jpg' width='140' height='200' />

Chapter 4 Lyapunov Stability - Hanyangccrs.hanyang.ac.kr/webpage_limdj/nonlinear/Chapter4Lec1.pdf · conditions for stability is called a Lyapunov function. The surface v (x) —

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