Guaranteed Cost Output Feedback Control of Fuzzy Systems via LMI Approach

Abstract

This paper is concerned with the stability with guaranteed cost for a fuzzy system with immeasurable premise variables via output feedback. It is well known that Takagi-Sugeno fuzzy model describes a wide class of nonlinear systems especially when its premise variables include immeasurable functions. However, when it comes to output feedback control design of such a fuzzy system, a conventional Parallel Distributed Compensator (PDC) is not feasible because the PDC shares the same immeasurable premise variables as those of a fuzzy system. In this paper, we introduce an output feedback controller with the estimate of the premise variables of an original fuzzy system. We then formulate the stabilization problem with guaranteed cost for a fuzzy system with immeasurable premise variables. Our control design method is based on a set of strict LMI conditions. No tuning parameter is necessary a priori to solve them. The stability with guaranteed cost takes care of not only stabilization but also control performance. Our proposed method attempts to minimize the upper bound of the performance index, which results in the satisfactory trajectories of the system. Finally, numerical examples are given to illustrate our control design method.