A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

Matteo Rubagotti, Luca Zaccarian, Alberto Bemporad

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

Original languageEnglish
Pages (from-to)950-959
Number of pages10
JournalInternational Journal of Control
Volume89
Issue number5
DOIs
Publication statusPublished - May 3 2016

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Lyapunov methods
Model predictive control
Lyapunov functions
Asymptotic stability
Closed loop systems
Linear programming

Keywords

  • Hybrid systems
  • piecewise-affine systems
  • stability analysis

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

Cite this

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains. / Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto.

In: International Journal of Control, Vol. 89, No. 5, 03.05.2016, p. 950-959.

Research output: Contribution to journalArticle

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