Exact stability analysis of 2-D systems using LMIs

Yoshio Ebihara, Yoshimichi Ito, Tomomichi Hagiwara

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

In this note, we propose necessary and sufficient conditions for the asymptotic stability analysis of two-dimensional (2-D) systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions that enable us to analyze the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that, by employing the generalized S-procedure, we can derive smaller size of LMIs so that the computational burden can be reduced.

Original languageEnglish
Pages (from-to)1509-1513
Number of pages5
JournalIEEE Transactions on Automatic Control
Volume51
Issue number9
DOIs
Publication statusPublished - Sep 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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