Convex sufficient conditions on asymptotic stability and l2 gain performance for uncertain discrete-time switched linear systems

Weiming Xiang, Jian Xiao

Research output: Contribution to journalArticle

Abstract

In this brief article, the stability and disturbance attenuation property in the sense of l2 gain for switched linear discrete-time systems are investigated. The computation of l2 gains against dwell time has been viewed as an open problem so far. A novel dwell-time dependent Lyapunov function (DTDLF) is introduced to study the stability and l2 gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, thus it is capable to be generalised to switched systems with uncertainties. Then, as an application, the H control problem is considered. Based on the DTDLF approach, the control synthesis procedures including state-feedback controllers and switching law design are unified into one-step method that explicitly facilitates the control synthesis process. Finally, numerical examples are provided to illustrate the proposed results.

Original languageEnglish (US)
Pages (from-to)211-218
Number of pages8
JournalIET Control Theory and Applications
Volume8
Issue number3
DOIs
StatePublished - Feb 20 2014
Externally publishedYes

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Switched Linear Systems
Dwell Time
Lyapunov functions
Asymptotic stability
Asymptotic Stability
Linear systems
Discrete-time
Lyapunov Function
Sufficient Conditions
Synthesis
State feedback
One-step Method
Discrete-time Linear Systems
Disturbance Attenuation
Switched Systems
State Feedback
Control Problem
Open Problems
Controllers
Controller

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Control and Optimization
  • Electrical and Electronic Engineering

Cite this

Convex sufficient conditions on asymptotic stability and l2 gain performance for uncertain discrete-time switched linear systems. / Xiang, Weiming; Xiao, Jian.

In: IET Control Theory and Applications, Vol. 8, No. 3, 20.02.2014, p. 211-218.

Research output: Contribution to journalArticle

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