Stochastic stability of genetic regulatory networks with a finite set delay characterization.

In this paper, the delay-distribution-dependent stability is derived for the stochastic genetic regulatory networks (GRNs) with a finite set delay characterization and interval parameter uncertainties. One important feature of the obtained results here is that the time-varying delays are assumed to be random and the sum of the occurrence probabilities of the delays is assumed to be 1. By employing a new Lyapunov-Krasovskii functional dependent on auxiliary delay parameters which allow the time-varying delays to be not differentiable, less conservative mean-square stochastic stability criteria are obtained. Finally, two examples are given to illustrate the effectiveness and superiority of the derived results.