Lyapunov function

Suppose we are given an autonomous system of first order differential equationsMathworldPlanetmath.


Let the origin be an isolated critical point of the above system.

A functionMathworldPlanetmath V(x,y) that is of class C1 and satisfies V(0,0)=0 is called a Lyapunov functionMathworldPlanetmath if every open ball Bδ(0,0) contains at least one point where V>0. If there happens to exist δ* such that the function V˙, given by


is positive definitePlanetmathPlanetmath in Bδ*(0,0). Then the origin is an unstablePlanetmathPlanetmath critical point of the system.

Title Lyapunov function
Canonical name LyapunovFunction
Date of creation 2013-03-22 13:42:29
Last modified on 2013-03-22 13:42:29
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 34-00
Synonym Liapunov function