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On the estimation of the domain of attraction for discrete-time switched and hybrid nonlinear systems

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  • Chuen Kit Luk
  • Graziano Chesi

Abstract

This paper addresses the estimation of the domain of attraction for discrete-time nonlinear systems where the vector field is subject to changes. First, the paper considers the case of switched systems, where the vector field is allowed to arbitrarily switch among the elements of a finite family. Second, the paper considers the case of hybrid systems, where the state space is partitioned into several regions described by polynomial inequalities, and the vector field is defined on each region independently from the other ones. In both cases, the problem consists of computing the largest sublevel set of a Lyapunov function included in the domain of attraction. An approach is proposed for solving this problem based on convex programming, which provides a guaranteed inner estimate of the sought sublevel set. The conservatism of the provided estimate can be decreased by increasing the size of the optimisation problem. Some numerical examples illustrate the proposed approach.

Suggested Citation

  • Chuen Kit Luk & Graziano Chesi, 2015. "On the estimation of the domain of attraction for discrete-time switched and hybrid nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(15), pages 2781-2787, November.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:15:p:2781-2787
    DOI: 10.1080/00207721.2013.879232
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    Cited by:

    1. Messaoud Aloui & Faiçal Hamidi & Houssem Jerbi & Mohamed Omri & Dumitru Popescu & Rabeh Abbassi, 2021. "A Chaotic Krill Herd Optimization Algorithm for Global Numerical Estimation of the Attraction Domain for Nonlinear Systems," Mathematics, MDPI, vol. 9(15), pages 1-30, July.

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