Variance-constrained filtering for discrete-time genetic regulatory networks with state delay and random measurement delay

This paper is concerned with the variance-constrained filtering problem for a class of discrete-time genetic regulatory networks (GRNs) with state delay and random one-step measurement delay. The phenomenon of the random one-step measurement delay is characterised by a random variable, which is assumed to obey the Bernoulli distribution with known occurrence probability. The purpose of the addressed problem is to design a filter such that, in the presence of state delay and random one-step measurement delay, an upper bound of the filtering error covariance matrix can be obtained and the explicit expression of the filter gain matrix is given. Then, the proposed variance-constrained filtering method can be used to approximate the concentrations of mRNAs and proteins. Finally, a numerical example is provided to illustrate the effectiveness of the designed filtering scheme.