New robust stability analysis for genetic regulatory networks with random discrete delays and distributed delays

This paper investigates the delay-probability-distribution-dependent stability problem of stochastic genetic regulatory networks (GRNs) with random discrete time delays and distributed time delays which exist in both translation process and feedback regulation process. The information of the probability distribution of the discrete time delays is considered and transformed into parameter matrices of the GRN models. By introducing a new Lyapunov functional which takes into account the ranges of delays and employing some free-weighting matrices, some new delay-probability-distribution-dependent stability criteria are established in the form of linear matrix inequalities (LMIs) to guarantee the GRNs to be asymptotically stable in the mean square. In addition, when estimating the upper bounds of the derivative of Lyapunov functionals, we carefully handle the additional useful terms about the distributed delays, which may lead to the less conservative results. The new criteria are applicable to both slow and fast time delays. Finally, numerical examples are given to illustrate the effectiveness of our theoretical results and less conservativeness of the proposed method.