Delay-dependent filter design for stochastic genetic regulatory networks in presence of time-varying delays

This paper addresses robust state estimation problem for Genetic Regulatory Networks (GRNs). A delay-dependent robust filter is designed for a realistic nonlinear stochastic model of GRN. The model provided is the most complete model used in the literature so far, in the sense that delays are time-varying, parameter uncertainties (time-varying and norm-bounded) are considered, stochastic noises appear at the state equations as well as the measurement equations. Besides, stochastic noise and disturbance are considered simultaneously in this model. Using a proper Lyapunov-Krasovskii functional based on delay decomposition approach, sufficient conditions for the existence of the filter are derived in terms of linear matrix inequality (LMI). These conditions ensure robust asymptotic mean square stability of the filtering error dynamics with a prescribed disturbance attenuation level. By use of delay decomposition approach and using a lemma containing a stochastic integral inequality, the obtained conditions are delay-dependent and have less conservativeness. The filter parameters are determined then, as the solution of another LMI. A simulation study is also given to show the effectiveness of the proposed filter design procedure.