Delay-dependent robust H∞H∞ filtering of uncertain stochastic genetic regulatory networks with mixed time-varying delays

In this paper, the robust H∞H∞ filtering problem for uncertain stochastic genetic regulatory networks (GRNs) with mixed time-varying delays is involved. The uncertain stochastic GRNs under consideration are extended to involve Itô-type stochastic disturbance, norm-bounded parameter uncertainties, and time-varying discrete and distributed delays. By constructing a proper Lyapunov–Krasovskii functional and using reciprocal convex technique, sufficient conditions in terms of linear matrix inequalities were presented to guarantee that the filtering error systems are mean-square robustly asymptotically stable with disturbance attenuation level γ. In the end, two numerical examples are given to illustrate the effectiveness of the proposed approach.