Novel Stability Criteria for T--S Fuzzy Systems

In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existi...

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Bibliographic Details
Published inIEEE transactions on fuzzy systems Vol. 22; no. 2; pp. 313 - 323
Main Authors Xudong Zhao, Lixian Zhang, Peng Shi, Karimi, Hamid Reza
Format Journal Article
LanguageEnglish
Published New York IEEE 01.04.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Criteria
Educational institutions
Fuzzy systems
Lyapunov function
Lyapunov functions
Lyapunov methods
Mathematical analysis
Mathematical models
membership-dependent
Polynomials
Stability
Stability criteria
Takagi-Sugeno (T-S) fuzzy system
Vectors
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Summary:In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature. Then, new membership-dependent stability conditions are developed by the new Lyapunov function approach. It is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical results.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2013.2254491