Geodesic
Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
Kybernetika, Tome 46 (2010) no. 1, pp. 19-37.

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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.
Classification : 34A34, 34A38, 34D20, 34D23, 34D35, 37B25, 70K20, 93D20
Keywords: maximal Lyapunov functions; domain of attraction; hybrid systems 
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     title = {Determining the domain of attraction of hybrid non{\textendash}linear systems using maximal {Lyapunov} functions},
     journal = {Kybernetika},
     pages = {19--37},
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     zbl = {1194.34018},
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Rozgonyi, Szabolcs; Hangos, Katalin M.; Szederkényi, Gábor. Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions. Kybernetika, Tome 46 (2010) no. 1, pp. 19-37. http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a1/