Necessary and sufficient conditions to stability of discrete-time delay systems

Tao Wang, Weiming Xiang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper is concerned with the stability analysis of discrete-time linear systems with time-varying delays. The novelty of this paper lies in that a novel Lyapunov–Krasovskii functional that updates periodically along with the time is proposed to reduce the conservatism and eventually be able to achieve the non-conservativeness in stability analysis. It can be proved that the stability of a discrete-time linear delay system is equivalent to the existence of a periodic Lyapunov–Krasovskii functional. Two necessary and sufficient stability conditions in terms of linear matrix inequalities are proposed in this paper. Furthermore, the novel periodic Lyapunov–Krasovskii functional is employed to solve the ℓ2-gain performance analysis problem when exogenous disturbance is considered. The effectiveness of the proposed results is illustrated by several numerical examples.

Original languageEnglish (US)
Pages (from-to)9788-9803
Number of pages16
JournalJournal of the Franklin Institute
Issue number16
StatePublished - Nov 2019

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics


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