Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach
Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach
复制标题
具有 SUM 调节逻辑的遗传网络的稳定性：Lur'e 系统和 LMI 方法
DOI：
10.1109/tcsi.2006.883882
复制
发表时间：
2006-11-01
影响因子：
5.1
通讯作者：
Aihara, Kazuyuki
中科院分区：
文献类型：
--
作者：
Li, Chunguang;Chen, Luonan;Aihara, Kazuyuki
在本文中，我们提出了一个非线性模型的基因调控网络与SUM调控功能。我们表明，遗传网络可以转化为Lur'e形式。基于李雅普诺夫方法和Lur 'e系统方法，遗传网络的稳定性的充分条件，特别是对于由于转录，翻译和易位的缓慢过程的时间延迟的情况下，和由于自然的随机内和细胞间波动的随机扰动的情况下，推导。所有的稳定性条件都是以线性矩阵不等式的形式给出的，易于验证。为了检验我们理论结果的有效性，本文还给出了几个遗传网络的例子。
In this paper, we present a nonlinear model for genetic regulatory networks with SUM regulatory functions. We show that the genetic network can be transformed into Lur'e form. Based on the Lyapunov method and the Lur'e system approach, sufficient conditions for the stability of the genetic networks are derived, in particular for the cases with time delays owing to the slow processes of transcription, translation, and translocation, and for the cases with stochastic perturbations due to natural random intra- and inter-cellular fluctuations. All the stability conditions are given in terms of linear matrix inequalities (LMIs), which are very easy to be verified. To test the effectiveness of our theoretical results, several examples of genetic networks are also presented in this paper.