An LMI approach to fuzzy controller designs based on relaxed stability conditions

Author

Tanaka, Kazuo ; Ikeda, Takayuki ; Wang, Hua O.

Author_Institution

Dept. of Human & Mech. Syst. Eng., Kanazawa Univ., Japan

Volume

1

fYear

1997

fDate

1-5 Jul 1997

Firstpage

171

Abstract

New stability conditions satisfying decay rate are derived for both continuous and discrete fuzzy control systems. LMI (linear matrix inequality) based design procedures that consider decay rate and constraints on control input and output are constructed using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate and constraints on control input and output. Design examples demonstrate the effectiveness of the LMI-based designs proposed in this paper

Keywords

Lyapunov methods; compensation; control system synthesis; distributed control; feedback; fuzzy control; nonlinear systems; optimisation; stability; Lyapunov function; Takagi-Sugeno models; convex optimization; feedback; fuzzy control; linear matrix inequality; nonlinear systems; parallel distributed compensation; stability conditions; Fuzzy control; Fuzzy sets; Fuzzy systems; Input variables; Linear matrix inequalities; Lyapunov method; Mechanical systems; Nonlinear systems; Stability; Takagi-Sugeno model;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems, 1997., Proceedings of the Sixth IEEE International Conference on

Conference_Location

Barcelona

Print_ISBN

0-7803-3796-4

Type

conf

DOI

10.1109/FUZZY.1997.616364

Filename

616364