Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties

In this paper, we investigate the problem of robust state estimator design for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time varying delays and randomly occurring uncertainties. By introducing a new discretized Lyapunov–Krasovskii functional together with a free-weighting matrix technique, first we derive a set of sufficient conditions for the existence of global asymptotic state estimator for the discrete-time GRN model with time delays satisfying both the lower and the upper bound of the interval time-varying delay. Further, the obtained results are extended to deal the robust state estimator design for the discrete-time GRN model in the presence of randomly occurring uncertainties which obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The proposed criterions are established in terms of linear matrix inequalities (LMIs) which can be easily solved via Matlab LMI toolbox. Finally, the robust state estimator design has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained theory.