PDC synthesis for T-S fuzzy large-scale systems

This paper deals with the decentralized stabilization problem for a T-S fuzzy large-scale system. The interconnection between any two subsystems may be nonlinear and satisfies some matching condition. The decentralized parallel distributed compensation (PDC) fuzzy control for each subsystem is synthesized in which the control gain depends on the strength of interconnections, maximal number of the fired rule in each subsystem and the common positive matrix P_i. Based on Lyapunov criterion and Riccati-inequality, and some sufficient conditions are derived and the common P_i is solved by linear matrix inequalities (LMI) toolbox of Matlab so that the whole closed-loop large-scale fuzzy system with the synthesized fuzzy control is asymptotically stable. Furthermore, we also discuss the robustness of the closed loop system with perturbations. Finally, a numerical example is given to illustrate the control synthesis and its effectiveness.