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

Szabolcs Rozgonyi; Katalin M. Hangos; Gábor Szederkényi

Kybernetika (2010)

  • Volume: 46, Issue: 1, page 19-37
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Rozgonyi, Szabolcs, Hangos, Katalin M., and Szederkényi, Gábor. "Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions." Kybernetika 46.1 (2010): 19-37. <http://eudml.org/doc/37706>.

@article{Rozgonyi2010,
abstract = {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.},
author = {Rozgonyi, Szabolcs, Hangos, Katalin M., Szederkényi, Gábor},
journal = {Kybernetika},
keywords = {maximal Lyapunov functions; domain of attraction; hybrid systems; domain of attraction; maximal Lyapunov functions; hybrid systems},
language = {eng},
number = {1},
pages = {19-37},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions},
url = {http://eudml.org/doc/37706},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Rozgonyi, Szabolcs
AU - Hangos, Katalin M.
AU - Szederkényi, Gábor
TI - Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 1
SP - 19
EP - 37
AB - 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.
LA - eng
KW - maximal Lyapunov functions; domain of attraction; hybrid systems; domain of attraction; maximal Lyapunov functions; hybrid systems
UR - http://eudml.org/doc/37706
ER -

References

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