\(H_\infty\) filtering for discrete-time genetic regulatory networks with random delay described by a Markovian chain
Summary: 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 [\textit{A. Liu} et al., Math. Biosci. 239, No. 1, 97--105 (2012; Zbl 1319.92028)].
discrete-time genetic regulatory networks
scientific article; zbMATH DE number 7022016
scientific article