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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 261353, 9 pages
http://dx.doi.org/10.1155/2013/261353
Research Article

LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

1Institution of Mathematics, Yibin University, Yibin, Sichuan 644007, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Received 27 June 2013; Accepted 6 August 2013

Academic Editor: Chuanzhi Bai

Copyright © 2013 Ruofeng Rao and Zhilin Pu. 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.

Abstract

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.