A Sampled-data Approach to Robust H∞ State Estimation for Genetic Regulatory Networks with Random Delays

This paper is concerned with the robust H∞ state estimation problem for a class of uncertain genetic regulatory networks (GRNs) with random delays and external disturbances by using sample-data method. An important feature of this paper is that the time-varying delays are assumed to be random and their probability distributions are known a priori. By substituting the continuous measurements, the sampled measurements are used to estimate the concentrations of mRNAs and proteins. On the basis of the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced. Then, some sufficient conditions are derived in terms of a set of linear matrix inequalities (LMIs), which ensure that the error system is globally asymptotically stable in the meansquare sense and satisfies H∞ performance. Further, the explicit expression of the required estimator gain matrices is proposed. Finally, a numerical example is used to illustrate the effectiveness and feasibility of the obtained estimation method.