Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram 624 302, Tamilnadu, India.
Math Biosci. 2013 Aug;244(2):165-75. doi: 10.1016/j.mbs.2013.05.003. Epub 2013 May 23.
This paper is concerned with the state estimation problem for delayed genetic regulatory networks (GRNs) based on passivity analysis approach. The main purpose of the problem is to design the estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. Time-varying delays are explicitly assumed to be non-differentiable and constraint on the derivative of the time-varying delay is less than one can be removed. Based on the Lyapunov-Krasovskii functionals involving triple integral terms, using some integral inequalities and convex combination technique, a delay-dependent passivity criterion is established for GRNs in terms of linear matrix inequalities (LMIs) that can efficiently be solved by any available LMI solvers. Finally, numerical examples and simulation are presented to demonstrate the efficiency of the proposed estimation schemes.
本文关注基于无源分析方法的时滞遗传调控网络（GRN）的状态估计问题。该问题的主要目的是设计估计器，通过可用的测量输出来近似 mRNA 和蛋白质的真实浓度。显式假设时变延迟不可微，并且可以去除时变延迟导数的约束小于一。基于涉及三积分项的 Lyapunov-Krasovskii 泛函，使用一些积分不等式和凸组合技术，以线性矩阵不等式（LMIs）的形式为 GRN 建立了时滞相关的无源准则，这些准则可以通过任何可用的 LMI 求解器有效地求解。最后，通过数值示例和仿真验证了所提出的估计方案的有效性。
