Robust stability of Markovian jumping genetic regulatory netwroks with mode-dependent delays

Zhang Wenbing; Fang Jianan; Tang Yang

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Robust stability of Markovian jumping genetic regulatory netwroks with mode-dependent delays

Zhang Wenbing 1 #,Fang Jianan 2 *,Tang Yang 1

1.School of Information Science and Technology,Donghua University

2.Shool of Information Science and Technology,Donghua University

*Correspondence author

#Submitted by

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Funding: the Research Fund for the doctoral Program of Higher Education（No.200802550007）, National Science Foundation of PR China（No.60874113）, the Key project of Shanghai Education Community（No.09ZZ66）, the Key Basic Research of Shanghai（No.09JC1400700）

Opened online:12 October 2010

Accepted by: none

Citation: Zhang Wenbing,Fang Jianan ,Tang Yang .Robust stability of Markovian jumping genetic regulatory netwroks with mode-dependent delays[OL]. [12 October 2010] http://en.paper.edu.cn/en_releasepaper/content/4387185

In this paper, 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 exist 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 inequalities. Illustrative examples are exploited to show the effectiveness of the derived LMIs(linear matrix inequalities)-based stability conditions.

Keywords:genetic regulatory network;delay-dependent;mode-dependent delays;Markovian jumping;LMIs

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