Nonconservative Lifted Convex Conditions for Stability of Discrete-Time Switched Systems Under Minimum Dwell-Time Constraint

Weiming Xiang, Hoang Dung Tran, Taylor T. Johnson

Research output: Contribution to journalArticle

4 Scopus citations


In this note, a novel conception called virtual clock, which is defined by an artificial timer over a finite cycle, is introduced for stability analysis of discrete-time switched linear systems under minimum dwell-time constraint. Two necessary and sufficient conditions associated with a virtual clock with a sufficient length are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. For the two nonconservative stability criteria, the lifted version maintains the convexity in system matrices. Based on the lifted convex conditions, the extensions to ℓ2-gain computation and ℋ control problems are presented in the sequel. In particular, a novel virtual-clock-dependent controller is designed, which outperforms the traditional mode-dependent and common gain controllers. Several numerical examples are provided to illustrate our theoretic results.

Original languageEnglish (US)
Article number8521694
Pages (from-to)3407-3414
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number8
StatePublished - Aug 2019
Externally publishedYes



  • Dwell time
  • stability
  • switched system
  • ℋ control
  • ℓ-gain

ASJC Scopus subject areas

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

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