H∞ State estimation for delayed discrete-time GRNs

This chapter is concerned with the problem of H∞ state estimation for a class of discrete-time GRNs with random delay and external disturbance. The random delay is described by a Markovian chain. The aim is to estimate the concentrations of mRNAs and proteins by designing H∞ filter based on available measurement outputs. By using the LKF method, a sufficient LMI condition is first established to ensure the filtering error system to be stochastically stable with a prescribed H∞ disturbance attenuation level. The condition is dependent on the transition probability matrix of the random delay. Then, the filter gains are represented via a feasible solution of the LMIs. Moreover, an optimization problem with LMIs constraints is established to design an H∞ filter which ensures an optimal H∞ disturbance attenuation level. The effectiveness of the proposed approach is illustrated by a numerical example.