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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 897280, 10 pages
http://dx.doi.org/10.1155/2014/897280
Research Article

Exponential Stability Analysis for Genetic Regulatory Networks with Both Time-Varying and Continuous Distributed Delays

1School of Control Science and Engineering, Shandong University, Jinan 250061, China
2School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Received 23 December 2013; Revised 8 March 2014; Accepted 9 March 2014; Published 6 May 2014

Academic Editor: Sanyi Tang

Copyright © 2014 Lizi Yin and Yungang Liu. 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 exponential stability is investigated for genetic regulatory networks with time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, new conditions of delay-dependent stability are obtained in the form of linear matrix inequality (LMI). The lower bound of derivatives of time-varying delay is first taken into account in genetic networks stability analysis, and the main results with less conservatism are established by interactive convex combination method to estimate the upper bound of derivative function of the Lyapunov-Krasovskii functional. In addition, two numerical examples are provided to illustrate the effectiveness of the theoretical results.