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

Fingerprint

Normal matrix
Fuzzy systems
Fuzzy Systems
Lyapunov Function
Linear Time
Lyapunov functions
Switching Systems
Invariant
Sufficient Conditions
Global Asymptotic Stability
Quadratic Function
Subsystem
Switching systems
Equivalence
Asymptotic stability
Necessary Conditions
Demonstrate
Class

Keywords

  • Asymptotic stability
  • Switching systems

ASJC Scopus subject areas

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

Cite this

On the stability of fuzzy systems. / Thathachar, M. A.L.; Viswanath, Pramod.

In: IEEE Transactions on Fuzzy Systems, Vol. 5, No. 1, 01.12.1997, p. 145-151.

Research output: Contribution to journalArticle

Thathachar, M. A.L. ; Viswanath, Pramod. / On the stability of fuzzy systems. In: IEEE Transactions on Fuzzy Systems. 1997 ; Vol. 5, No. 1. pp. 145-151.
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