Robust filtering of extended stochastic genetic regulatory networks with parameter uncertainties, disturbances, and time-varying delays

This paper addresses robust H∞ filtering problem for a nonlinear genetic regulatory network (GRN), which is extended to include noise and disturbances, parameter uncertainties, and time-varying delays simultaneously. It is assumed that the nonlinear function that describes the feedback regulation satisfies the sector-bounded condition, the stochastic state perturbation is in the form of a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. To account for the unavoidable modeling errors and parameter fluctuations, the network parameters are assumed to be time-varying but norm-bounded values. We aim to estimate the true concentrations of mRNAs and proteins by designing a linear filter such that, for all admissible uncertainties, nonlinearities, stochastic perturbations and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square sense while achieving the prescribed H∞ disturbance attenuation level. By using the Lyapunov stability theory and Itoˆ formula, sufficient conditions for the existence of the filter are obtained in the form of a linear matrix inequality (LMI). Then, explicit expressions for the desired filter gains are provided. Finally, a simulation example is given in order to illustrate the effectiveness of the proposed design procedure.