This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

这项工作涉及通过被动控制受到混合时间延迟的随机遗传调节网络 (GRN) 的问题，其中混合时间延迟包括泄漏、离散和分布式延迟。本文的主要目的是在脉冲扰动下构建一个基于被动的标准，以便所提出的 GRN 是随机稳定的。基于Lyapunov泛函方法和Jensen积分不等式，我们以LMI的形式获得了一组新的基于被动性的新的基于延迟的充分条件，可以通过现有的数值软件来确定。最后，我们提出了数值模拟来证明所提出方法的有效性。