Control synthesis of singularly perturbed fuzzy systems

This paper considers the problem of designing stabilizing and H∞ controllers for nonlinear singularly perturbed systems described by Takagi-Sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e. For the synthesis problem of simultaneously designing the bound of e and stabilizing or H∞ controllers, linear matrix inequalities (LMI)- based methods are presented. For evaluating the upper bound of e subject to stability or a prescribed H∞ performance bound constraint for the resulting closed-loop system, sufficient conditions are developed, respectively. For the stabilizing and H∞ control synthesis without the consideration of improving the bound of e, new design methods are also given in terms of solutions to a set of LMIs. Examples are given to illustrate the efficiency of the proposed methods.