Delay-dependent filter design for nonlinear delayed genetic regulatory networks with intrinsic and extrinsic noises

This paper investigates a delay-dependent L₂ - L_∞ filter design method for genetic regulatory networks (GRNs). The purpose of the addressed problem is to design a linear filter that can estimate the true concentrations of gene products such as mRNAs and proteins. At first, a nonlinear delayed GRN model is considered under intrinsic and extrinsic noises simultaneously in order to reflect the inherent intracellular and extracellular noises. The stochastic intrinsic noise is in the form of a scalar Brownian motion. By using a stochastic integral inequality and the Lyapunov stability theory, delay-dependent sufficient conditions for the existence of the filter are obtained in the form of linear matrix inequalities (LMIs), which ensure the filtering error dynamics is asymptotically mean square stable with a prescribed L₂ - L_∞ attenuation level. Then, explicit expressions for the desired filter parameters are provided. Finally, a three-node GRN is presented to show the effectiveness of the proposed design procedure.