Control Synthesis of Singularly Perturbed Fuzzy Systems

This paper considers the problem of designing stabilizing and Hinfincontrollers 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 Hinfincontrollers, linear matrix inequalities (LMI)- based methods are presented. For evaluating the upper bound of e subject to stability or a prescribed Hinfinperformance bound constraint for the resulting closed-loop system, sufficient conditions are developed, respectively. For the stabilizing and Hinfincontrol 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.