A descriptor system approach to fuzzy guaranteed cost control system design

This paper studies the problem of guaranteed cost control for a Takagi-Sugeno (T-S) fuzzy system by descriptor system method. The redundancy property of a T-S descriptor system is utilized to simplify the control design issue. Furthermore, a linear quadratic cost function is considered as the performance index of the T-S fuzzy control system. According to the redundancy property, the control design of a descriptor system often leads to fewer stability conditions. Consequently, the T-S fuzzy system herein is presented as the descriptor system form. Then, the guaranteed cost fuzzy control for the descriptor subsystem is synthesized by parallel distributed compensation (PDC). Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs) method, some sufficient conditions are derived to obtain the local state feedback gains of the PDC such that the whole fuzzy descriptor system is not only asymptotically stable but also cost guaranteed. Finally, a practical example is given to illustrate the effectiveness of the proposed criterion.