School of Information Science and Engineering, Central South University, Changsha 410083, PR China.
Math Biosci. 2012 Mar;236(1):53-63. doi: 10.1016/j.mbs.2012.01.005. Epub 2012 Feb 3.
This paper deals with the problem of stabilization design and H(∞) control for a class of genetic regulatory networks (GRNs) with both intrinsic perturbation and extrinsic perturbation. Some delay-dependent mean-square stabilization criteria are put forward for nominal systems and uncertain systems by using an improved free-weighting matrix approach. As a result, the corresponding stabilization controllers and H(∞) controllers of GRNs are constructed with time delays compensated and suboptimal solutions are obtained via exploiting an iterative procedure together with the linear matrix inequality (LMI) method and the cone complementarity liberalization (CCL) algorithm. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.
本文针对同时具有内扰和外扰的一类基因调控网络（GRN）的稳定设计和 H(∞)控制问题进行了研究。通过采用改进的自由加权矩阵方法，提出了标称系统和不确定系统的时滞相关均方稳定判据。结果，通过利用迭代过程以及线性矩阵不等式（LMI）方法和锥互补松弛（CCL）算法，为 GRN 构建了具有时滞补偿的相应稳定控制器和 H(∞)控制器，并获得了次优解。最后，通过三个数值例子验证了所提出的理论结果的有效性。
