Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays

In this paper, the event-triggered H∞H∞ state estimation problem is investigated for a class of discrete-time stochastic genetic regulatory networks with both Markovian jumping parameters and time-varying delays. The jumping parameters are governed by a homogeneous Markovian chain and the time-varying delays under consideration occur in both the feedback regulatory process and transcription process. The aim of this paper is to estimate the concentrations of mRNA and protein in such genetic regulatory networks by using the available measurement outputs. In order to reduce the information communication burden, the event-triggered mechanism is adopted and the measurement outputs are only transmitted to the estimator when a certain triggered condition is met. By constructing an appropriate Lyapunov functional, some sufficient conditions are derived under which the estimation error dynamics is stochastically stable and the H∞H∞ performance constraint is satisfied. Based on the analysis results, the desired H∞H∞ estimator parameters are designed in terms of the solution to a set of matrix inequalities that can be easily solved by the Matlab toolboxes. Finally, a simulation example is provided to illustrate the effectiveness of the proposed event-triggered state estimation scheme.