ESTIMATING THE REGION OF ATTRACTION FOR AN AUTONOMOUS SYSTEM WITH CPA LYAPUNOV FUNCTIONS

Abstract

Lyapunov Converse Theorems only tell us the sufficient conditions for the existence of a Lyapunov function in a nonconstructive way. They are helpless to construct such a function. Recently, constructing Continuous Piecewise Affine (CPA) Lyapunov functions has been developed. Basing on this technique, we can construct one. Then, this construction can help us to find a very exact estimate of the region of attraction. This is the main result of the paper. We use the method to estimate the region of attraction for the case of the asymptotical stability. We study this technique for the case autonomous systems.