Robust stability analysis of stochastic genetic regulatory networks with discrete and distributed delay in both mRNA and protein dynamics

This paper addresses robust stability of genetic regulatory networks (GRNs) with stochastic perturbation and discrete and distributed time-varying delays. Aside from discrete delays, there are few results about stability of GRNs with distributed delay. In this paper, noise perturbation and delays have been considered in both mRNA and protein dynamics. Based on Lyapunov functional approach and linear matrix inequality (LMI) techniques, sufficient conditions are established to guarantee the robust stability of genetic regulatory networks. Stability conditions are derived in the form of LMIs, which are very easy to be verified. An example is presented to verify the theoretical results.