Department of Automation, Zhejiang University of Technology, Zhejiang Provincial United Key Laboratory of Embedded Systems, Hangzhou 310023, PR China.
Math Biosci. 2012 Sep;239(1):97-105. doi: 10.1016/j.mbs.2012.05.002. Epub 2012 May 28.
The H(∞) filtering problem is investigated in this paper for a class of discrete-time genetic regulatory networks (GRNs) with random delays. The addressed filtering problem is to estimate the concentrations of mRNA and protein, and the filtering error system is modeled as a Markovian switched system. By using a properly constructed Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs), which can guarantee stochastic stabilization of the filtering error system. Then, an optimization problem with LMIs constraints is established to design an H(∞) filter which ensures an optimal H(∞) disturbance attenuation level. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.
本文针对一类具有随机时滞的离散时间基因调控网络（GRN），研究了 H(∞)滤波问题。所研究的滤波问题旨在估计 mRNA 和蛋白质的浓度，并且滤波误差系统被建模为马尔可夫切换系统。通过使用适当构造的李雅普诺夫函数，以线性矩阵不等式（LMI）的形式给出了一个充分条件，该条件可以保证滤波误差系统的随机稳定性。然后，建立了一个具有 LMI 约束的优化问题，以设计一个 H(∞)滤波器，确保最优的 H(∞)干扰衰减水平。最后，给出了一个实例来说明所提出的结果的有效性。
