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Determining the domain of attraction of hybrid non-linear systems using maximal Lyapunov functions. (English) Zbl 1194.34018

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:
 34A38 Hybrid systems 34D20 Stability of ODE