Stability and stabilization of nonlinear systems andTakagi‐Sugeno′s fuzzy models

Abstract

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.