Li Ping, Lam James, Shu Zhan
Department of Mechanical Engineering, The University of Hong Kong, Hong Kong.
IEEE Trans Syst Man Cybern B Cybern. 2010 Apr;40(2):336-49. doi: 10.1109/TSMCB.2009.2022402. Epub 2009 Oct 23.
This paper is concerned with the transient and steady-state estimates of a class of genetic regulatory networks (GRNs). Some sufficient conditions, which do not only present the transient estimate but also provide the estimates of decay rate and decay coefficient of the GRN with interval parameter uncertainties (interval GRN), are established by means of linear matrix inequality (LMI) and Lyapunov-Krasovskii functional. Moreover, the steady-state estimate of the proposed GRN model is also investigated. Furthermore, it is well known that gene regulation is an intrinsically noisy process due to intracellular and extracellular noise perturbations and environmental fluctuations. Then, by utilizing stochastic differential equation theory, the obtained results are extended to the case with noise perturbations due to natural random fluctuations. All the conditions are expressed within the framework of LMIs, which can easily be computed by using standard numerical software. A three-gene network is provided to illustrate the effectiveness of the theoretical results.
本文关注一类基因调控网络（GRNs）的瞬态和稳态估计。通过线性矩阵不等式（LMI）和Lyapunov-Krasovskii泛函，建立了一些充分条件，这些条件不仅给出了瞬态估计，还提供了具有区间参数不确定性的GRN（区间GRN）的衰减率和衰减系数估计。此外，还研究了所提出的GRN模型的稳态估计。此外，众所周知，由于细胞内和细胞外的噪声扰动以及环境波动，基因调控是一个本质上有噪声的过程。然后，利用随机微分方程理论，将所得结果扩展到存在自然随机波动引起的噪声扰动的情况。所有条件都在LMI框架内表示，可以使用标准数值软件轻松计算。提供了一个三基因网络来说明理论结果的有效性。
