State estimation for Markovian jumping genetic regulatory networks with random delays

• A new system model for GRNS with Markovian jumping parameters and random delays is proposed.
• The stability criteria of the estimation error system are obtained in the form of LMIs.
• The explicit expression of the desired estimator is shown.
• A numerical example is presented to show the effectiveness of the proposed results.

In this paper, the state estimation problem is investigated for stochastic genetic regulatory networks (GRNs) with random delays and Markovian jumping parameters. The delay considered is assumed to be satisfying a certain stochastic characteristic. Meantime, the delays of GRNs are described by a binary switching sequence satisfying a conditional probability distribution. The aim of this paper is to design a state estimator to estimate the true states of the considered GRNs through the available output measurements. By using Lyapunov functional and some stochastic analysis techniques, the stability criteria of the estimation error systems are obtained in the form of linear matrix inequalities under which the estimation error dynamics is globally asymptotically stable. Then, the explicit expression of the desired estimator is shown. Finally, a numerical example is presented to show the effectiveness of the proposed results.