Stability Analysis And Reachability Set Estimation Of Switched Gene Regulatory Networks With Mixed Time Delays

Genetic regulatory network(GRN)is a mechanism gene expressions in an organism.The main processes of gene expression are gene transcription and m RNA translation.Since the transcription and translation are so slow that time delay is one of important factors impacting dynamics of GRNs.Due to the relevant biological background and genetic engineering,GRNs with time delays have attracted attention of many academics and others.This article mainly studies the stability analysis and reachable set estimation problems of switching GRN with mixed time delays.The main research contents are as follows:First,the global exponential stability of the switching GRN with mixed time delays is studied.The present results related to stability analysis of the switching GRNs are generally obtained by constructing Lyapunov-Krasovskii functional.In this article,based on the definition of global exponential stability,the global exponential stability criteria are obtained.The obtained stability criteria only need to calculate the eigenvalues of a constant matrix or solve several simple linear matrix inequalities can be implemented by using standard software tools.Finally,several numerical examples illustrate the effectiveness of the proposed method.Secondly,the reachable set estimation problem of switching GRNs with mixed time delays and bounded disturbances is studied.A new sufficient condition is proposed to ensure that the state trajectories are contained in a Cartesian product of polytopes or balls.Compared with the conditions obtained by the traditional Lyapunov-Krasovskii functional method,this sufficient condition only needs to solve several simple linear matrix inequalities with 2n variables,and reduces the computational complexity,which can be easily implemented by standard tool software.In addition,an optimization method is proposed to guarantee that the Cartesian product is as small as possible.Finally,the results of the numerical example illustrate the effectiveness of the proposed method.