This paper deals with the delay-probability-distribution-dependent state estimation problem for discrete-time genetic regulatory networks (DGRNs) with random time-varying delays. As an important feature the time-varying delays are assumed to be random and their probability distributions are known a priori. The information of probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred DGRNs model. Based on the Lyapunov–Krasovskii functional approach, a delay-probability-distribution-dependent sufficient condition is obtained in terms of linear matrix inequalities (LMIs) such that estimation errors are robustly globally asymptotically stable in the mean-square sense for all admissible uncertainties. The probability distribution dependent delays are introduced to reflect more realistic dynamical behaviors of DGRNs. Finally numerical examples are provided to substantiate the theoretical results.
