Delay-dependent filtering for stochastic nonlinear genetic regulatory networks with time-varying delays and extrinsic noises

In this paper, the delay-dependent filtering problem is investigated for a more realistic nonlinear genetic regulatory network (GRN) with time-varying delays, stochastic intrinsic noises and extrinsic noise, where the stochastic noises exist in both the state dynamics and measurement equations. The purpose of the addressed filtering problem is to estimate the true concentrations of gene products such as mRNAs and proteins. Specifically, we are interested in designing a delay-dependent L₂-L_∞ linear filter such that for all admissible nonlinearities, time-varying delays as well as intrinsic and extrinsic noises, the filtering error dynamics is asymptotically mean square stable with a prescribed L₂-L_∞ attenuation level. The delay decomposition approach is first used to derive sufficient conditions in the form of linear matrix inequalities (LMIs) that guarantee the desired filtering performance, and the filter gains are then characterized as the solution to a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the theoretical results.