On the stability of fuzzy systems

M. A.L. Thathachar, Pramod Viswanath

Research output: Contribution to journalArticle

Abstract

This paper studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary condition and a sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI subsystems. A particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic Lyapunov function. A constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided.

Original languageEnglish (US)
Pages (from-to)145-151
Number of pages7
JournalIEEE Transactions on Fuzzy Systems
Volume5
Issue number1
DOIs
StatePublished - Dec 1 1997
Externally publishedYes

Keywords

  • Asymptotic stability
  • Switching systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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