Further improvement of free-weighting matrices technique for systems with time-varying delay

Yong He, Qing Gao Wang, Lihua Xie, Chong Lin

Research output: Contribution to journalArticlepeer-review

753 Citations (Scopus)


A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Original languageEnglish
Pages (from-to)293-299
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number2
Publication statusPublished - Feb 2007
Externally publishedYes


  • Augmented Lyapunov functional
  • Delay-dependent
  • Linear matrix inequality (LMI)
  • Stability
  • Time-varying delay

ASJC Scopus subject areas

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


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