Non-fragile observer design for discrete-time genetic regulatory networks with randomly occurring uncertainties

This paper investigates the problem of non-fragile observer design for a class of discrete-time genetic regulatory networks (DGRNs) with time-varying delays and randomly occurring uncertainties. A non-fragile observer is designed, for estimating the true concentration of mRNAs and proteins from available measurement outputs. One important feature of the results obtained that are reported here is that the parameter uncertainties are assumed to be random and their probabilities of occurrence are known a priori. On the basis of the Lyapunov–Krasovskii functional approach and using a convex combination technique, a delay-dependent estimation criterion is established for DGRNs in terms of linear matrix inequalities (LMIs) that can be efficiently solved using any available LMI solver. Finally numerical examples are provided to substantiate the theoretical results. (paper)