Determining the domain of attraction of hybrid non-linear systems using maximal lyapunov functions

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22 Citations (Scopus)

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 Vn 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 Mathematicapackage to find such Lyapunov functions Vn 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.

Original languageEnglish
Pages (from-to)19-37
Number of pages19
JournalKybernetika
Volume46
Issue number1
Publication statusPublished - Jun 21 2010

Keywords

  • Domain of attraction
  • Hybrid systems
  • Maximal lyapunov functions

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Information Systems
  • Artificial Intelligence
  • Electrical and Electronic Engineering

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