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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 of ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
Software:
Mathematica
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References:
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