Kybernetika 46 no. 1, 19-37, 2010

Determining the domain of attraction of hybrid non-linear systems using maximal Lyapunov functions

Szabolcs Rozgonyi, Katalin M. Hangos and Gábor Szederkényi


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 \textit{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.


domain of attraction, maximal Lyapunov functions, hybrid systems


34D20, 34D23, 34D35, 37B25, 34A34, 70K20