Delay-dependent stochastic stability for Markov-type genetic regulatory network with partial information on transition probabilities

This paper focuses on the stability problem of Markov-type genetic regulatory network (GRN) with partial information on transition probabilities. This situation is called defective statistics of modes transition. By considering the effect of time-varying delay on switched system and the relationship between mRNA and protein in the augmented Lyapunov-Krasovskii function (LKF), weakening the conditions of constructing LKF and using extended Wirtinger´s inequality and free-connection weighting method to deal with their weak infinitesimal operator, the less conservative stability criteria are obtained. Finally, numerical examples are given to illustrate the effectiveness and the merits of the proposed method.