Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 168962, 14 pages
Research Article

A T-S Fuzzy Model-Based Adaptive Exponential Synchronization Method for Uncertain Delayed Chaotic Systems: An LMI Approach

Department of Automotive Engineering, Seoul National University of Science and Technology, 172 Gongneung 2-dong, Nowon-gu, Seoul 139-743, Republic of Korea

Received 22 April 2010; Revised 30 July 2010; Accepted 21 September 2010

Academic Editor: Ondřej Došlý

Copyright © 2010 Choon Ki Ahn. 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 proposes a new fuzzy adaptive exponential synchronization controller for uncertain time-delayed chaotic systems based on Takagi-Sugeno (T-S) fuzzy model. This synchronization controller is designed based on Lyapunov-Krasovskii stability theory, linear matrix inequality (LMI), and Jesen's inequality. An analytic expression of the controller with its adaptive laws of parameters is shown. The proposed controller can be obtained by solving the LMI problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed method.