Disturbance attenuation analysis for Markovian jump genetic regulatory networks with mode dependent delays

Since only small numbers of molecules are involved in gene regulation, genetic regulatory networks are extremely sensitive to stochastic fluctuations. Gene networks also suffer from delay due to slowness of biochemical reactions and molecular translocation. In this paper, we investigate stochastic stability and disturbance attenuation of stochastic Markovian genetic regulatory network with mode dependent delay. By using Lyapunov-Krasovskii functional, delay dependent conditions of stochastic stability and disturbance attenuation of genetic network is derived. These conditions are in the form of linear matrix inequality which can be verified easily by MATLAB.