Answered: Verify that V = x† + 2x3 + 2x,x2 + xỉ…

Verify that V = x† + 2x3 + 2x,x2 + xỉ is a Lyapunov function for the system described by the following state equations dx1 = X2 dt dx2 = -X2 - xỉ. dt Then, check the stability of the system.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 5CC

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Question

Verify that
V = xf + 2x3 + 2x, xX, + xỉ
is a Lyapunov function for the system described by the following state
equations
dx1
= X2
dt
dx2
-X2 - xỉ.
dt
Then, check the stability of the system.

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