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Stability analysis of genetic regulatory networks via a linear parameterization approach
Complex & Intelligent Systems ( IF 5.8 ) Pub Date : 2021-02-02 , DOI: 10.1007/s40747-020-00245-1
Shasha Xiao , Zhanshan Wang

This paper investigates the problem of finite-time stability (FTS) for a class of delayed genetic regulatory networks with reaction-diffusion terms. In order to fully utilize the system information, a linear parameterization method is proposed. Firstly, by applying the Lagrange’s mean-value theorem, the linear parameterization method is applied to transform the nonlinear system into a linear one with time-varying bounded uncertain terms. Secondly, a new generalized convex combination lemma is proposed to dispose the relationship of bounded uncertainties with respect to their boundaries. Thirdly, sufficient conditions are established to ensure the FTS by resorting to Lyapunov Krasovskii theory, convex combination technique, Jensen’s inequality, linear matrix inequality, etc. Finally, the simulation verifications indicate the validity of the theoretical results.



中文翻译:

通过线性参数化方法对遗传调控网络进行稳定性分析

本文研究了一类带有反应扩散项的时滞遗传调控网络的时限稳定性(FTS)问题。为了充分利用系统信息,提出了一种线性参数化方法。首先,通过应用拉格朗日均值定理,采用线性参数化方法将非线性系统转换为具有时变有界不确定项的线性系统。其次,提出了一种新的广义凸组合引理来处理有界不确定性与其边界的关系。第三,通过利雅普诺夫·克拉索夫斯基理论,凸组合技术,詹森不等式,线性矩阵不等式,为确保FTS建立了充分条件。

更新日期:2021-02-02
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