Robust 渭-stability analysis of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays

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• 作者：Xiaodi Li^a ; ^{sodymath@163.com} ; R. Rakkiyappan^b ; C. Pradeep^c
• 关键词：Stochastic genetic regulatory network ; Uncertain parameter ; Markovian jumping parameter ; LMI ; Lyapunov method ; Unbounded time-varying delay
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 期刊代码：89_10075704
• 类别：ph
• 出版时间：October, 2012
• 卷：17
• 期：10
• 页码：3894-3905
• 文件大小：416 K

摘要

This paper investigates the global robust stability problem of Markovian switching uncertain stochastic genetic regulatory networks with unbounded time-varying delays and norm bounded parameter uncertainties. The structure variations at discrete time instances during the process of gene regulations known as hybrid genetic regulatory networks based on Markov process is proposed. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The concept of global robust 渭-stability in the mean square for genetic regulatory networks is given. Based on Lyapunov function, stochastic theory and It么鈥檚 differential formula, the stability criteria are presented in the form of linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the effectiveness of the main result.