Stability and stabilization of nonlinear systems and Takagi-Sugeno's fuzzymodels

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 usi ng a quadratic Liapunov candidate function. This paper proposes a relaxatio n of Tanaka's stability condition: unlike related works, the equations to b e solved are not Liapunov equations for each rule matrix, but a convex comb ination of them. The coefficients of this sums depend on the membership fun ctions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among wh ich the Parallel Distributed Compensation (PDC). An application to the inve rted pendulum is proposed here.