Estimaación del dominio de atracción de sistemas no lineales mediante modelos borrosos polinomiales

Abstract

Many approaches in fuzzy systems literature express LMI conditions for a Takagi-Sugeno model and finish the problem once those conditions are feasible. However, studying the obtained region of attraction and its relationship with the original nonlinear problem is forgotten. This paper proposes to obtain a predefined-shape zone, as large as possible, belonging to the local domain of attraction of the origin of a nonlinear system. In order to do this, local fuzzy polynomial models are used whose analysis can be carried out by convex optimization (sum of squares). Moreover membership information is used in order to do iterations with the fuzzy modeling region, maximizing the size of the proven domain of attraction, which reduces conservatism over existing results.