Robust Exponential Stability and Disturbance Attenuation for Discrete-Time Switched Systems under Arbitrary Switching

Weiming Xiang, Hoang Dung Tran, Taylor T. Johnson

Research output: Contribution to journalArticle

Abstract

In this note, the global exponential stability of discrete-time switched systems under arbitrary switching is investigated. First, for discrete-time switched nonlinear systems, the global exponential stability is found to be equivalent to the existence of an M-step sequence with sufficient length and a family of Lyapunov functions, and then a stability criterion is proposed for the nominal linear case in the framework of quadratic Lyapunov function. In order to extend the stability criterion to handle uncertainties, an equivalent condition which has a promising feature that is convex in system matrices is derived, leading to a robust stability criterion for uncertain discrete-time switched linear systems. Moreover, also taking the advantage of the convex feature, the disturbance attenuation performance in the sense of -gain is studied. Several numerical examples are provided to illustrate our approach.

Original languageEnglish (US)
Pages (from-to)1450-1456
Number of pages7
JournalIEEE Transactions on Automatic Control
Volume63
Issue number5
DOIs
StatePublished - May 2018
Externally publishedYes

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Stability criteria
Asymptotic stability
Lyapunov functions
Linear systems
Nonlinear systems

Keywords

  • 2-gain
  • Arbitrary switching
  • stability
  • switched system
  • uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

Robust Exponential Stability and Disturbance Attenuation for Discrete-Time Switched Systems under Arbitrary Switching. / Xiang, Weiming; Tran, Hoang Dung; Johnson, Taylor T.

In: IEEE Transactions on Automatic Control, Vol. 63, No. 5, 05.2018, p. 1450-1456.

Research output: Contribution to journalArticle

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