H∞ filtering for discrete-time genetic regulatory networks with random delays

The H(∞) filtering problem is investigated in this paper for a class of discrete-time genetic regulatory networks (GRNs) with random delays. The addressed filtering problem is to estimate the concentrations of mRNA and protein, and the filtering error system is modeled as a Markovian switched system. By using a properly constructed Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs), which can guarantee stochastic stabilization of the filtering error system. Then, an optimization problem with LMIs constraints is established to design an H(∞) filter which ensures an optimal H(∞) disturbance attenuation level. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.