Robust state estimation for discrete-time genetic regulatory network with random delays

• This paper investigates state estimation problem for discrete-time genetic regulatory networks (DGRNs) with time-varying delays and parameter uncertainties.
• A state estimator is designed to estimate the gene states such that the error dynamics is robust globally asymptotically stable.
• State estimation condition is dependent on the probability distribution of the time delays by introducing the stochastic variable.
• Numerical simulations are exploited to illustrate the applicability and usefulness of the developed theoretical results.

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.