On the stability of fuzzy systems

M. A.L. Thathachar; Pramod Viswanath

doi:10.1109/91.554461

On the stability of fuzzy systems

M. A.L. Thathachar, Pramod Viswanath

Research output: Contribution to journal › Article › peer-review

83 Scopus citations

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 language	English (US)
Pages (from-to)	145-151
Number of pages	7
Journal	IEEE Transactions on Fuzzy Systems
Volume	5
Issue number	1
DOIs	https://doi.org/10.1109/91.554461
State	Published - 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

Keywords

Asymptotic stability
Switching systems

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10.1109/91.554461

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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.",

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AU - Viswanath, Pramod

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AB - 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.

KW - Asymptotic stability

KW - Switching systems

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JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

IS - 1

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On the stability of fuzzy systems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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