Decentralized guaranteed cost control synthesis in fuzzy interconnected systems

This paper studies the problem of guaranteed cost control for a nonlinear interconnected system which is composed by a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. A linear quadratic cost function is considered as the performance index of the closed-loop fuzzy interconnected system. Then, the decentralized guaranteed cost fuzzy control for each rule of the subsystem is synthesized by parallel distributed compensation (PDC). Based on the Lyapunov criterion and linear matrix inequalities (LMIs) method, some sufficient conditions are derived to obtain the local state feedback gain of the PDC control such that the whole closed-loop fuzzy interconnected system is not only asymptotically stable but also cost guaranteed. Finally, we give a practical example to illustrate the effectiveness of the proposed criterion.