Pandiselvi S, Raja R, Cao Jinde, Rajchakit G, Ahmad Bashir
1Department of Mathematics, Alagappa University, Karaikudi, India.
2Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, India.
Adv Differ Equ. 2018;2018(1):123. doi: 10.1186/s13662-018-1569-z. Epub 2018 Apr 3.
This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.
这项工作主要针对具有泄漏、分布式和概率测量延迟的离散时间随机遗传调控网络，标记了状态变量的近似问题。在此，我们设计了一种线性估计器，使得mRNA和蛋白质的吸收能够通过已知测量输出进行近似。通过利用李雅普诺夫 - 克拉索夫斯基泛函和一些随机分析方法，我们在线性矩阵不等式结构下获得了估计误差系统的稳定性公式，在该公式下估计误差动态是鲁棒指数稳定的。此外，所获得的条件（以线性矩阵不等式的形式）可以通过一些可用的软件包轻松求解。而且，所需估计器的具体表达式也在主要部分给出。最后，给出了两个数学示例以展示所提出概念结果的优势。
