Exponential state estimation for discrete-time switched genetic regulatory networks with random delays

Abstract

This paper is concerned with the problem of state estimator design for a class of discrete-time switched genetic regulatory networks (GRNs) with random time delays. The involved time delays are assumed to be randomly time-varying and are modeled by introducing Bernoulli distributed sequences. By using a piecewise Lyapunov–Krasovskii functional together with the linear matrix inequality (LMI) approach, we design a delay-distributed dependent state estimator such that the estimation error system is globally exponentially stable. Further, a class of switching signals specified by the average dwell time is identified to guarantee the exponential state estimation. All the conditions are established in the framework of LMIs, which can easily be solved by using standard numerical software. If a set of LMIs are feasible, then the desired state estimator can be obtained. Finally, a numerical example with simulation result is provided for the GRN model to illustrate the applicability and usefulness of the obtained theory.