Set-membership filtering for genetic regulatory networks with missing values

The data missing is a common and important problem in the area of genetic regulatory networks (GRNs). A class of discrete-time GRNs with missing values, parameter uncertainties, time delays and molecular noise is considered in this paper. A set-membership filtering method is proposed to estimate the states of the underlying GRNs. Meanwhile, the corresponding problem of set-membership filtering is formulated as finding the set of estimations that belongs to an ellipsoid. The desired filter gains are characterized as the solution of a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method, which shows that by using the proposed set-membership filtering algorithm, the concentrations of mRNA and protein could be estimated accurately.