Delay independent stability of linear switching systems with time delay

Sehjeong Kim, Sue Ann Campbell, Xinzhi Liu

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)

Abstract

We consider a switching system with time delay composed of a finite number of linear delay differential equations (DDEs). Each DDE consists of a sum of a linear ODE part and a linear DDE part. We study two particular cases: (a) all the ODE parts are stable and (b) all the ODE parts are unstable and determine conditions for delay independent stability. For case (a), we extend a standard result of linear DDEs via the multiple Lyapunov function and functional methods. For case (b) the standard DDE result is not directly applicable, however, we are able to obtain uniform asymptotic stability using the single Lyapunov function and functional methods.

Original languageEnglish
Pages (from-to)785-801
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume339
Issue number2
DOIs
Publication statusPublished - Mar 15 2008
Externally publishedYes

Keywords

  • Delay differential equations
  • Lyapunov functional
  • Switching systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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