GLOBAL EXPONENTIAL STABILITY ANALYSIS OF DISCRETE-TIME GENETIC REGULATORY NETWORKS WITH TIME DELAYS

This paper focuses on the study of global robust exponential stability of discrete-time genetic regulatory networks (GRNs) with time-invariant/time-varying delays and parameter uncertainties. Many existing results on this problem are based on the linear matrix inequality (LMI) approach, which needs to verify whether there exists a feasible solution of a set of LMIs. Along with the increase in the number of genes, dimensions of LMIs will increase accordingly, which will lead to a large amount of calculation. Based on M-matrix theory, sufficient conditions ensuring the global robust exponential stability of a class of discrete-time GRNs with time-invariant/time-varying delays and parameter uncertainties are presented. These given conditions are to check whether a constructed constant matrix is a nonsingular M-matrix. Simulation results of several examples are given to demonstrate the validity of the proposed method.