Improved Control Design of Discrete-Time Takagi-Sugeno Fuzzy Systems

The stability and stabilization are one of the important control problems. This paper proposes a new design method of a stabilizing controller for discrete-time Takagi-Sugeno fuzzy systems so that the controller stabilizes a larger class of nonlinear system than ever. Different from the conventional parallel distributed compensator (PDC), a novel non-PDC controller is introduced. The controller employs not only the current state variables of the system but also the past ones for the feedback. In order for the controller to be feasible for a wide class of nonlinear systems, a new Lyapunov function which has delayed variables as well is adopted to obtain asymptotic stability conditions of the fuzzy system with the controller. The relaxation lemmas are applied to make less conservate in such asymptotic stability conditions. In addition to the theoretical analysis and synthesis, examples are considered. The proposed design method and the existing ones are compared by such numerical examples to show the validity of the proposed control design procedures.