DETERMINING THE DOMAIN OF ATTRACTION OF HYBRID NON-LINEAR SYSTEMS USING MAXIMAL LYAPUNOV FUNCTIONS

作者：Rozgonyi Szabolcs^*; Hangos Katalin M; Szederkenyi Gabor

来源：Kybernetika, 2010, 46(1): 19-37.

• maximal Lyapunov functions
• domain of attraction
• hybrid systems

In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions V(n) in a rational functional form approximating a maximal Lyapunov function V(M) that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions V(n) for a class of hybrid (piecewise non-linear) systems, where the dynamics is continuous on the boundary of the different regimes in the state space.
In addition, a computationally feasible method is proposed to estimate the DOA using a maximal fitting hypersphere.

• 出版日期2010