Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 605794, 20 pages
Research Article

Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

1State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
2Institute of Electrical Engineering, Yanshan University, Qinhuangdao City 066004, China

Received 14 October 2010; Revised 14 February 2011; Accepted 25 February 2011

Academic Editor: Ilmar Ferreira Santos

Copyright © 2011 Chun-xia Dou 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.


A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribed disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence of robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimized performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.