Guaranteed Cost Control Design Based on Takagi-Sugeno Fuzzy Systems with Nonlinear Subsystems

This paper is concerned with guaranteed cost control design for a generalized Takagi-Sugeno fuzzy system. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations, while a generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems. For such a generalized system, a design method of a stabilizing controller with guaranteed cost is proposed by introducing a new class of non-PDC controllers. Non-PDC controller is a generalized controller of PDC one, which is a traditional fuzzy controller. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.