Decentralized Control of Uncertain Fuzzy Large-Scale System with Time Delay and Optimization

Abstract

This paper studies the decentralized stabilization problem for an uncertain fuzzy large-scale system with time delays. The considered large-scale system is composed of several T-S fuzzy subsystems. The decentralized parallel distributed compensation (PDC) fuzzy control for each subsystem is designed to stabilize the whole system. Based on Lyapunov criterion, some sufficient conditions are proposed. Moreover, the positive definite matrices $P_i$ and PDC gain $K_{ij}$ can be solved by linear matrix inequality (LMI) toolbox of Matlab. Then, the optimization design method for decentralized control is also considered with respect to a quadratic performance index. Finally, numerical examples are given and compared with those of Zhang et al., 2004 to illustrate the effectiveness and less conservativeness of our method.