Exponential H_∞ filtering for switched stochastic genetic regulatory networks with random sensor delays

The exponential H_∞ filtering problem is investigated in this paper for a class of switching-type stochastic genetic regulatory networks (GRNs) with random sensor delays. The objective is to estimate the true concentrations of the mRNA and protein in the presence of random sensor delays. By using the average dwell time approach, sufficient conditions are derived to ensure the filtering error dynamics are mean-square exponentially stable with a prescribed H_∞ disturbance attenuation level. The filter gains are given in terms of the solution to a set of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed design method.