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Mathematical Problems in Engineering
Volume 2015, Article ID 303918, 5 pages
http://dx.doi.org/10.1155/2015/303918
Research Article

Analysis on Global Asymptotical Stability of Genetic Regulatory Networks with Time-Varying Delays via Convex Combination Method

1Department of Computer Engineering, Sichuan Vocational and Technical College of Communications, Chengdu 611130, China
2College of Automation, Chongqing University, Chongqing 400044, China
3Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China

Received 7 June 2014; Accepted 22 July 2014

Academic Editor: Chuandong Li

Copyright © 2015 Yang Liu and Haixia Wu. 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

The global asymptotical stability analysis for genetic regulatory networks with time delays is concerned. By using Lyapunov functional theorem, LMIs, and convex combination method, a new delay-dependent stability criterion has been presented in terms of LMIs to guarantee the delayed genetic regulatory networks to be asymptotically stable. The restriction that the derivatives of the time-varying delays are less than one is removed. Our result is applicable to both fast and slow time-varying delays. The stability criterion has less conservative and wider application range. Experimental result has been used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.