Stability analysis of uncertain genetic sum regulatory networks
Stability analysis of uncertain genetic sum regulatory networks
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DOI：
10.1016/j.automatica.2008.01.030
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发表时间：
2008-09-01
期刊：
影响因子：
6.4
通讯作者：
Hung, Y. S.
中科院分区：
文献类型：
--
作者：
Chesi, G.;Hung, Y. S.
研究具有和调节函数的不确定遗传网络的鲁棒稳定性问题。具体地说，我们首先考虑不确定的遗传网络，其中调控发生在转录水平，并通过引入不确定非线性的边界集推导出鲁棒稳定性的充分条件。因此，我们证明了这个条件可以通过多项式Lyapunov函数和利用多项式的平方矩阵表示（SMR）的边界集的多项式描述来表示为凸优化，这允许通过线性矩阵不等式（LMI）来确定多项式是否为平方和（SOS）。然后，我们提出了一种用凸优化方法计算一类边界集的方法。值得注意的是，尽管变量平衡点不能作为参数相关非线性方程组的解来计算，因此是未知的，但这些结果是推导出来的。最后，提出的方法被扩展到在不同水平发生调控的模型，并且mRNA和蛋白质动力学都是非线性的。(c) 2008 Elsevier Ltd.版权所有。
This paper addresses the problem of establishing robust stability of uncertain genetic networks with sum regulatory functions. Specifically, we first consider uncertain genetic networks where the regulation occurs at the transcriptional level, and we derive a sufficient condition for robust stability by introducing a bounding set of the uncertain nonlinearity. We hence show that this condition can be formulated as a convex optimization through polynomial Lyapunov functions and polynomial descriptions of the bounding set by exploiting the square matricial representation (SMR) of polynomials which allows to establish whether a polynomial is a sum of squares (SOS) via a linear matrix inequality (LMI). Then, we propose a method for computing a family of bounding sets by means of convex optimizations. It is worthwhile to remark that these results are derived in spite of the fact that the variable equilibrium point cannot be computed as being the solution of a system of parameter-dependent nonlinear equations, and is hence unknown. Lastly, the proposed approach is extended to models where the regulation occurs at different levels and both mRNA and protein dynamics are nonlinear. (c) 2008 Elsevier Ltd. All rights reserved.