H ∞ Filtering for Markovian Switching Genetic Regulatory Networks with Time-Delays and Stochastic Disturbances

Abstract

This paper is concerned with the H∞ filtering problem for a class of nonlinear Markovian switching genetic regulatory networks (GRNs) with time-delays, intrinsic fluctuation and extrinsic noise. The delays, which exist in both the translation process and feedback regulation process, are not dependent on the system model. The intrinsic fluctuation is described as a state-dependent stochastic process, while the extrinsic noise is modeled as an arbitrary signal with bounded energy, and no exact statistics about the noise are required to be known. The aim of the problem addressed is to design a Markovian jump linear filter to estimate the true concentrations of mRNA and protein through available measurement outputs. By resorting to the Lyapunov functional method and some stochastic analysis tools, it is shown that if a set of linear matrix inequalities (LMIs) is feasible, then the desired linear filter exists. The designed filter ensures asymptotic mean-square stability of the filtering error system and two prescribed L2-induced gains from the noise signals to the estimation errors. Finally, an illustrative example is given to demonstrate the effectiveness of the approach proposed.