H∞ state estimation for discrete time-delayed stochastic genetic regulatory networks with known sojourn probabilities

This paper investigates the problem of H_∞ state estimation for discrete-time stochastic genetic regulatory networks (GRNs) with switching parameters, time-varying delays, and exogenous disturbances. A new discrete-time stochastic GRN model with switching parameters is proposed by assuming that the sojourn probability of each subsystem of the GRN under consideration is known. By using the stochastic analysis approach, sufficient conditions are derived under which the augmented estimation error system is stochastically stable and satisfies a prescribed H_∞ disturbance attenuation level γ. The gain matrices of the desired state estimator can be obtained by solving a matrix inequality. A numerical example is given to illustrate the effectiveness of the designed state estimator.