I am studying Lyapunov stability. My question is really short, and it is:
Suppose I get a derivative of a Lyapunov function of the form:
$\dot{V}(x,y)=-x^5-y^2$
what can I conclude about the stability of the system?
2026-03-27 06:56:54.1774594614
How to analyze the derivative of a Lyapunov function
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I don't think you can conclude anything about the stability of the system.
The derivative changes its sign in any circle around the origin, so you can only conclude that your Lyapunov function is inconclusive for your system.