Consider the system x_1=x_2, x_2=-(x_1+x_2)- h (x_1+x_2) where h is continuously differentiable and zh(z) > 0 for all z not equal to 0. Using the variable gradient method, find a Lyapunov function that shows that the origin is globally asymptotically stable.

Consider the system x_1=x_2, x_2=-(x_1+x_2)- h (x_1+x_2) where h is continuously differentiable and zh(z) > 0 for all z not equal to 0. Using the variable gradient method, find a Lyapunov function that shows that the origin is globally asymptotically stable.

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

Consider the system x_1=x_2,

x_2=-(x_1+x_2)- h (x_1+x_2)

where h is continuously differentiable and zh(z) > 0 for all z not equal to 0. Using the variable

gradient method, find a Lyapunov function that shows that the origin is globally

asymptotically stable.

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