Dissipativity-Based Filtering for Switched Genetic Regulatory Networks with Stochastic Disturbances and Time-Varying Delays

This paper deals with the problem of dissipativity-based filtering for switched genetic regulatory networks (GRNs) with stochastic perturbation and time-varying delays. By choosing an appropriate piecewise Lyapunov function and using the average dwell time method, we propose a new set of sufficient conditions in terms of Linear matrix inequalities (LMIs) for the existence of dissipative filter, which ensures that the resulting filtering error system is mean-square exponentially stable with dissipativity performance. The filter gains are provided by solving feasible solutions to a certain set of LMIs. A simulation example is given to demonstrate the effectiveness of the desired dissipativity-based filter design approach.

1 Introduction

Genetic regulatory networks (GRNs) are the mechanisms that evolved to regulated the expression of genes, where the expression level of a gene is regulated negatively or positively by their own produced proteins [1]. Understanding gene expression regulation has an immediate impact on biology and medicine because many traits and diseases are related to dysfunctional transcriptional regulators or mutations in regulatory sequences [19], [24], [41]. With the development of DNA microarray technology [25], it is possible to measure gene expression levels on a genomic scale and widely applied to the analysis of gene transcription. Based on the theoretical analysis for the results of experiments, some GRNs models have been proposed [3], [6], [7].