Spherical domain of attraction estimation for nonlinear systems

Abstract

This work proposes an algorithm to obtain a predefined-shape zone as large as possible, belonging to the local domain of attraction of a nonlinear system. In order to do it, fuzzy polynomial models will be used which analysis can be done by convex optimization (sum of squares). Most fuzzy control papers check LMI or SOS stability conditions for Takagi-Sugeno fuzzy models and, if feasibility is reached, forget to study the obtained region and its relationship with the original nonlinear problem. Having into account the shape of the membership functions in a particular region of interest, less conservative stability and stabilization conditions can be easily set up for doing iterations with the fuzzy modelling region in order to maximize the proved basin of attraction.