Stability analysis of standard genetic regulatory networks with time-varying delays and stochastic perturbations

In this paper, the stability analysis problem is investigated for a standard class of genetic regulatory networks (GRNs) with stochastic disturbances and time-varying delays. The standard GRNs under consideration are based on the model of the recurrent neural networks, the stochastic perturbation is in the form of a scalar Brownian motion, and the time-varying delays exist in the transcription and translation processes. Specifically, we are interested in (1) establishing a standard model for the time-varying delayed GRNs and (2) establishing conditions under which the standard GRNs are exponentially mean-square stable in the presence of time delays and stochastic disturbances. By using the linear matrix inequality (LMI) technique and S-procedure, sufficient conditions are first derived for ensuring globally asymptotic and exponential stability that can be easily solved by using standard software packages. Two numerical examples are exploited to demonstrate the effectiveness of the proposed method.