Robust state estimation for discrete-time stochastic genetic regulatory networks with probabilistic measurement delays

In this paper, the robust H∞ state estimation problem is investigated for a class of discrete-time stochastic genetic regulatory networks (GRNs) with probabilistic measurement delays. Norm-bounded uncertainties, stochastic disturbances and time-varying delays are considered in the discrete-time stochastic GRNs. Meantime, the measurement delays of GRNs are described by a binary switching sequence satisfying a conditional probability distribution. The main purpose is to design a linear estimator to approximate the true concentrations of the mRNA and the protein through the available measurement outputs. Based on the Lyapunov stability theory and stochastic analysis techniques, sufficient conditions are first established to ensure the existence of the desired estimators in the terms of a linear matrix inequality (LMI). Then, the explicit expression of the desired estimator is shown to ensure the estimation error dynamics to be robustly exponentially stable in the mean square and a prescribed H∞ disturbance rejection attenuation is guaranteed for the addressed system. Finally, a numerical example is presented to show the effectiveness of the proposed results.