Output feedback control design for nonlinear systems based on a generalized Takagi-Sugeno fuzzy system

This paper is concerned with output feedback 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 output feedback controller 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. Our 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. An observer, which estimates the state of the system using available information on the system, is also constructed. Then, we show that the separation principle holds, and an output feedback controller is obtained by combining the state feedback controller and observer. Finally, a numerical example is given to illustrate our nonlinear control design and to show the effectiveness over other existing results.