On the stability of fuzzy systems

Author

Thathachar, M. A L ; Viswanath, Pramod

Author_Institution

Indian Inst. of Sci., Bangalore, India

Volume

5

Issue

1

fYear

1997

fDate

2/1/1997 12:00:00 AM

Firstpage

145

Lastpage

151

Abstract

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

Keywords

Lyapunov methods; asymptotic stability; discrete time systems; fuzzy control; fuzzy systems; linear systems; matrix algebra; LTI switching systems; Lyapunov function; fuzzy systems; global asymptotic stability; linear time invariant systems; necessary condition; sufficient condition; Asymptotic stability; Fuzzy control; Fuzzy sets; Fuzzy systems; Lyapunov method; Robust stability; Sufficient conditions; Switching systems; Time varying systems; Uncertainty;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/91.554461

Filename

554461