Mathematical Problems in Engineering
Volume 7 (2001), Issue 3, Pages 221-240

Stability and stabilization of nonlinear systems and Takagi-Sugeno's fuzzy models

Yann Blanco, Wilfrid Perruquetti, and Pierre Borne

Lail Upresa 8021 CNRS, Ecole Centrale De Lille, BP48, Cité Scientifique, Villeneuve D'Ascq 59651, France

Received 15 August 2000; Revised 10 October 2000

Copyright © 2001 Yann Blanco et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper outlines a methodology to study the stability of Takagi-Sugeno's (TS) fuzzy models. The stability analysis of the TS model is performed using a quadratic Liapunov candidate function. This paper proposes a relaxation of Tanaka's stability condition: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them. The coefficients of this sums depend on the membership functions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among which the Parallel Distributed Compensation (PDC). An application to the inverted pendulum is proposed here.