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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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