Answered: Verify that V = x14+ 2x22+2x1x2 + x12…

Verify that V = x14+ 2x22+2x1x2 + x12 is a Lyapunov function for the system described by the following state equations dx1/dt = x2 dx2/dt= -x2 - x13. Then, check the stability of the system.

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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Question

Verify that

V = x1⁴+ 2x_2²+2x₁x₂ + x_1²

is a Lyapunov function for the system described by the following state
equations

dx_1/dt = x₂
dx₂/dt= -x₂ - x_1^3.

Then, check the stability of the system.

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