Relaxed Stability and Performance Conditions for Takagi–Sugeno Fuzzy Systems With Knowledge on Membership Function Overlap

Author

Sala, Antonio ; Arino, Carlos

Author_Institution

Dept. of Syst. Eng. & Control, Valencia Univ.

Volume

37

Issue

3

fYear

2007

fDate

6/1/2007 12:00:00 AM

Firstpage

727

Lastpage

732

Abstract

This correspondence presents a relaxation of some earlier linear matrix inequality (LMI) conditions, which allow setting up less conservative stability or performance conditions for Takagi-Sugeno fuzzy models. Unlike the previous literature, this correspondence takes into account the knowledge of the membership functions´ shape by considering bounds on them and their cross products (interpreted as an overlap measure), introducing auxiliary LMI variables. Numerical examples illustrate the achieved improvements

Keywords

fuzzy systems; linear matrix inequalities; nonlinear control systems; stability; Takagi-Sugeno fuzzy systems; auxiliary LMI variables; linear matrix inequality; membership function overlap; performance conditions; relaxed stability; Control systems; Distributed control; Fuzzy control; Fuzzy sets; Fuzzy systems; Linear matrix inequalities; Nonlinear systems; Shape control; Shape measurement; Stability; Linear matrix inequality (LMI); Takagi–Sugeno (TS) fuzzy control; nonlinear control; parallel distributed compensation (PDC); quadratic stability; relaxed condition; Algorithms; Computer Simulation; Markov Chains; Models, Statistical; Neural Networks (Computer); Nonlinear Dynamics; Pattern Recognition, Automated; Stochastic Processes;

fLanguage

English

Journal_Title

Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on

Publisher

ieee

ISSN

1083-4419

Type

jour

DOI

10.1109/TSMCB.2006.887949

Filename

4200815