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.