H∞ mode-independent filter design for Markovian jump genetic regulatory networks with time-varying delays

This paper investigates the problem of designing H∞ filter for gene regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. Since in real gene networks the current jump mode is not easily accessible, the filter parameters are considered to be independent from the current system mode. By using mode-dependent Lyapunov–Krasovski functionals, appropriate conditions for the stochastic stability and disturbance attenuation of mixed GRN/filter system is derived. Mode independent filter gains are then obtained from some sufficient conditions in the form of linear matrix inequalities which are easy to solve by numerical methods. In the end, a numerical example and the relevant simulations are presented to evaluate the results.