Title :
Relaxed stability conditions for Takagi-Sugeno´s fuzzy models
Author :
Blanco, Yann ; Perruquetti, Wilfrid ; Borne, Pierre
Author_Institution :
Ecole Centrale de Lille, Villeneuve d´´Ascq, France
Abstract :
This paper outlines a methodology to study the stability of Takagi-Sugeno´s fuzzy models using a systems of linear matrix inequalities (LMIs). The Takagi-Sugeno´s model is first introduced. A stability analysis is then performed using a quadratic Lyapunov candidate function. This paper proposes a relaxation of Tanaka´s stability condition: the LMIs to be solved are not Lyapunov equations for each rule matrix, but convex combinations of them. The coefficients of these sums depend on the membership functions. A generalization to the case of stabilization via parallel distributed compensation regulators is also proposed, with an application to a model of inverted pendulum
Keywords :
Lyapunov methods; compensation; fuzzy control; fuzzy set theory; matrix algebra; pendulums; stability; Lyapunov method; Takagi-Sugeno models; Tanaka stability condition; fuzzy control; fuzzy models; inverted pendulum; linear matrix inequality; membership functions; parallel distributed compensation; stability conditions; Petroleum; Regulators; Stability; Takagi-Sugeno model;
Conference_Titel :
Fuzzy Systems, 2000. FUZZ IEEE 2000. The Ninth IEEE International Conference on
Conference_Location :
San Antonio, TX
Print_ISBN :
0-7803-5877-5
DOI :
10.1109/FUZZY.2000.839050