Output Feedback Stabilization of Discrete-Time Fuzzy Systems

This paper is concerned with output feedback control design for a discrete-time Takagi-Sugeno fuzzy system where the premise variable is not necessarily measurable. The Takagi-Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations, and a fuzzy system to be considered in this paper describes even a wider class of nonlinear systems. For a fuzzy system, a design method of a stabilizing output feedback controller is proposed by employing a fuzzy multiple Lyapnunov functional and descriptor system approach. These techniques reduce the conservatism in stabilizing controller design conditions. Such conditions are given in terms of a set of linear matrix inequalities(LMIs), which are easily numerically solvable. In addition, a relaxation method is used to further reduce the conservatism in design conditions. A proposed controller can be of reduced-order, which is practically useful for large-scale systems. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.