Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 504378, 18 pages
http://dx.doi.org/10.1155/2012/504378
Research Article

Robust Stability of Markovian Jumping Genetic Regulatory Networks with Mode-Dependent Delays

Guang He,1 Jian-An Fang,2 and Xiaotai Wu1

1Department of Mathematics, Anhui Polytechnic University, Anhui, Wuhu 241000, China
2School of Information Science and Technology, Donghua University, Shanghai 201620, China

Received 28 August 2012; Revised 13 October 2012; Accepted 16 October 2012

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2012 Guang He 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.

Abstract

The robust stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks with parameter uncertainties and mode-dependent delays, which varies randomly according to the Markov state and exists in both translation and feedback regulation processes. The purpose of the addressed stability analysis problem is to establish some easily verifiable conditions under which the Markovian jumping genetic regulatory networks with parameter uncertainties and mode-dependent delays is asymptotically stable. By utilizing a new Lyapunov functional and a lemma, we derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks in the form of linear matrix inequalities. Illustrative examples are exploited to show the effectiveness of the derived linear-matrix-inequalities- (LMIS-) based stability conditions.