Relaxed stability conditions for Takagi-Sugeno´s fuzzy models

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