Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservati...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 356; pp. 44 - 62
Main Authors Yang, Xiaozhan, Lam, Hak-Keung, Wu, Ligang
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2019
Subjects
Convex polyhedron
Membership function
Stability analysis
T–S fuzzy system
T–S fuzzy system
Membership function
Stability analysis
Convex polyhedron
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Summary:This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2018.01.018