H∞ Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

Abstract

This paper is concerned with the $H_{\infty }$ filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to design $H_{\infty }$ filter to estimate the true concentrations of mRNAs and proteins based on available measurement data. By introducing an appropriate Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs) which makes the filtering error system stochastically stable with a prescribed $H_{\infty }$ disturbance attenuation level. The filter gains are given by solving the LMIs. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach; that is, our approach is available for a smaller $H_{\infty }$ disturbance attenuation level than one in (Liu et al., 2012).