By using the Liapunov function V(x, y, z) = x² + y? + z², show that the origin of thefollowing system is asymptotically stable.(* =-y-xy2 +z? – x3ý = x + z - y32 = -xz - x²z- yz2 - z5

To show that for the Lyapunov function the origin of the given system is asymptotically stable. If…

Answered: By using the Liapunov function V(x, y,…

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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By using the Liapunov function V(x, y, z) = x² + y? + z?, show that the origin of the following system is asymptotically stable. (* = -y-xy² + z² – x3 y = x+z-y 2 = -xz - x²z - yz? - z5