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Zbl 1194.34018
Rozgonyi, Szabolcs; Hangos, Katalin M.; Szederkényi, Gábor
Determining the domain of attraction of hybrid non-linear systems using maximal Lyapunov functions. (English)
[J] Kybernetika 46, No. 1, 19-37 (2010). ISSN 0023-5954

Summary: 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.

MSC 2000:: *34A38
34D20 Lyapunov stability of ODE

Keywords: domain of attraction; maximal Lyapunov functions; hybrid systems

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