A fuzzy Lyapunov approach to fuzzy control system design

Author

Tanaka, Kazuo ; Hori, Tsuyoshi ; Wang, Hua O.

Volume

6

fYear

2001

fDate

2001

Firstpage

4790

Abstract

This paper discusses the stability of Takagi-Sugeno fuzzy models via the so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on a fuzzy Lyapunov approach, we gives the stability conditions for open-loop fuzzy systems. All the conditions derived here are represented in terms of linear matrix inequalities (LMIs) and contain upper bounds of the time derivative of premise membership functions as LMI variables. Hence, the treatment of the upper bounds play an important and effective role in system analysis and design. In addition, relaxed stability conditions are also derived by considering the property of the time derivative of premise membership functions. Several analysis and design examples illustrate the utility of the fuzzy Lyapunov approach

Keywords

Lyapunov methods; control system synthesis; fuzzy control; fuzzy set theory; matrix algebra; stability; Lyapunov function; Takagi-Sugeno models; fuzzy control; linear matrix inequality; membership functions; stability; upper bounds; Fuzzy control; Fuzzy systems; Intelligent systems; Linear matrix inequalities; Lyapunov method; Marine vehicles; Mechanical engineering; Stability; Takagi-Sugeno model; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2001. Proceedings of the 2001

Conference_Location

Arlington, VA

ISSN

0743-1619

Print_ISBN

0-7803-6495-3

Type

conf

DOI

10.1109/ACC.2001.945740

Filename

945740