Three stability criteria for delayed stochastic genetic regulatory networks and their conservativeness analysis

This paper considers the problem of stability analysis of a class of delayed genetic regulatory networks (GRNs) with stochastic disturbances. By introducing appropriate Lyapunov-Krasovskii functional and employing free-weighting matrix approach, convex combination approach and delay-range partition approach, respectively, three stability criteria in the form of linear matrix inequalities are established to guarantee the considered GRNs to be asymptotically stable in the mean square sense. The change rate of time-varying delays is assumed to be less than infinity. So, these stability criteria are applicable to both fast and slow change rate of time-varying delays. Then, theoretical and numerical comparisons are given to evaluate the conservativeness of the proposed stability criteria.