Decentralized PDC for large-scale T-S fuzzy systems

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