Delay‐dependent robust dissipative filtering of stochastic genetic regulatory networks with time‐varying delays

This study deals with the problem of delay‐dependent dissipative filtering for genetic regulatory networks (GRNs) with norm‐bounded parameter uncertainties and time‐varying delays. It is assumed that the non‐linear function describing the feedback regulation satisfies the sector‐bounded condition. Improved delay‐dependent stochastic stability and filter design method for stochastic GRNs are obtained by applying the delay fractioning technique, Jensen inequalities and introducing some proper slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Sufficient conditions of the robust stability and filtering problems are proposed, respectively. The filter, which can guarantee the resulting error system to be asymptotically stable in the mean‐square sense and satisfy a prescribed performance level for all delays no larger than a given upper bound, are constructed. A numerical example is provided to demonstrate effectiveness of the proposed results in this study.