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On the Stability of Fuzzy Systems

Thathachar, MAL and Viswanath, Pramod (1997) On the Stability of Fuzzy Systems. In: IEEE Transactions on Fuzzy Systems, 5 (1). pp. 145-151.


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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 and 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.

Item Type: Journal Article
Publication: IEEE Transactions on Fuzzy Systems
Publisher: IEEE
Additional Information: Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Asymptotic stability;Switching systems
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 25 Aug 2008
Last Modified: 19 Sep 2010 04:25
URI: http://eprints.iisc.ac.in/id/eprint/6277

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