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- Consider the system d x= -x³ y² dt d dt = -2x²y³. Show that V(x, y) = x² + y² is a weak Lyapunov function for this system and explain why the origin is not asymptotically stable.

- Consider the system d x= -x³ y² dt d dt = -2x²y³. Show that V(x, y) = x² + y² is a weak Lyapunov function for this system and explain why the origin is not asymptotically stable.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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- Consider the system d x= -x³ y² dt d dt = -2x²y³. Show that V(x, y) = x² + y² is a weak Lyapunov function for this system and explain why the origin is not asymptotically stable.
Transcribed Image Text:- Consider the system d x= -x³ y² dt d dt = -2x²y³. Show that V(x, y) = x² + y² is a weak Lyapunov function for this system and explain why the origin is not asymptotically stable.
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