Asymptotic and robust stability of genetic regulatory networks with time-varying delays
Asymptotic and robust stability of genetic regulatory networks with time-varying delays
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DOI：
10.1016/j.neucom.2007.03.011
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发表时间：
2008-01-01
期刊：
影响因子：
6
通讯作者：
Cao, Jinde
中科院分区：
文献类型：
--
作者：
Ren, Fengi;Cao, Jinde
时滞在遗传网络的动力学中起着重要的作用，由于基因转录和翻译以及蛋白质在胞浆和细胞核之间的扩散等缓慢的生化反应，时延在遗传调控的建模中是不可忽视的。本文提出了一种基于和调控逻辑的延迟遗传调控网络(GRN)渐近稳定性的稳健分析方法，在和调控逻辑中，每个转录因子共同作用于一个基因，即所有输入的调控函数和。这里假定时间延迟是时变的，并且属于给定的间隔。基于Lyapunov稳定性理论和线性矩阵不等式(LMI)，给出了保证广义随机神经网络稳定的充分条件。所得到的条件是以LMI的形式导出的，易于通过LMI工具箱进行验证。最后给出了算例，说明了所得结果的有效性。(C)2007 Elsevier B.V.保留所有权利。
Time delay plays an important role in dynamics of genetic networks and cannot be ignored in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. This paper presents a robust analysis approach to asymptotic stability of the delayed genetic regulatory networks (GRNs) with SUM regulatory logic in which each transcription factor acts additively to regulate a gene, i.e., the regulatory function sums over all the inputs. Time delays here are assumed to be time-varying and belong to the given intervals. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability of the GRNs. The obtained conditions are derived in terms of LMIs which are easy to be verified via the LMI toolbox. Illustrative examples are presented to show the effectiveness of the obtained results. (c) 2007 Elsevier B.V. All rights reserved.