Mode-Dependent Filtering for Stochastic Markovian Switching Genetic Regulatory Networks with Leakage and Time-Varying Delays

In this paper, the filtering problem is considered for Markovian switching genetic regulatory networks (GRNs) with mode-dependent leakage and time-varying delays along intrinsic molecular fluctuations and extrinsic molecular noises. The aim of this paper is to design a filter to estimate the true concentrations of mRNAs and proteins. By choosing suitable Lyapunov-Krasovskii functionals and reciprocally convex combination approach, sufficient conditions are obtained to ensure that the filtering error system is globally stochastically stable in the mean-square sense with the prescribed disturbance attenuation levels. The existence of the designed filters is expressed in terms of linear matrix inequalities (LMIs), which can be easily solved by using Matlab LMI toolbox. Also the corresponding results are obtained for the GRNs without leakage delays. Finally, two numerical examples are given, which include a repressilator model of Escherichia coli to illustrate the effectiveness of the proposed theoretical results.