Sampled‐data H∞ filtering for stochastic genetic regulatory networks

Abstract

SUMMARYThis paper is concerned with the sampled‐data Hinfty filtering problem for a class of stochastic genetic regulatory networks with both extrinsic and intrinsic disturbances. The extrinsic disturbance and intrinsic noises are described, respectively, by an unknown signal with finite energy and a set of scalar Brownian motions. The expression levels of the mRNA and protein of the considered genetic regulatory network are sampled and then transmitted to the filter in order to estimate the states of the genetic network under consideration. The corresponding filtering error dynamics is then represented by means of a system with time‐varying delay. By constructing a simple yet practical Lyapunov functional that reflects all the information about the system complexity, sufficient conditions are established so as to guarantee both the exponential mean‐square stability and the H∞ performance for the filtering error dynamics. It is shown that the desired sampled‐data H∞ filter exists if certain matrix inequalities are solvable where the solvability can be readily checked by using the available software. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper. Copyright © 2011 John Wiley & Sons, Ltd.