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

Abstract EN

This paper is concerned with the H∞ filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance.

The aim is to design H∞ 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∞ 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∞ disturbance attenuation level than one in (Liu et al., 2012).