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Journal of Applied Mathematics
Volume 2012, Article ID 246705, 19 pages
Research Article

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

School of Information Science and Engineering, Central South University, Changsha 410075, China

Received 7 November 2011; Accepted 6 January 2012

Academic Editor: Huijun Gao

Copyright © 2012 Hang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 Pi and PDC gain Kij 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.