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

Szabolcs Rozgonyi, Katalin M. Hangos, Gábor Szederkényi (2010)

Kybernetika

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...

Practical Stability in Terms of Two Measures for Hybrid Dynamic Systems

Shurong Sun, Zhenlai Han, Elvan Akin-Bohner, Ping Zhao (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We study hybrid dynamic systems on time scales. Using Lyapunov-like functions, we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales.

The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations

Gastón Beltritti, Stefania Demaria, Graciela Giubergia, Fernando Mazzone (2025)

Czechoslovak Mathematical Journal

We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions.

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