New Stability Criteria for a Class of Markovian Jumping Genetic Regulatory Networks with Time-varying Delays

This paper addresses the problem of stability analysis for a class of genetic regulatory networks (GRNs) with Markovian jumping parameters and time-varying delays. By constructing a novel Lyapunov-Krasovskii functional (LKF) and using an appropriate enlargement scheme, new stability criteria are proposed in terms of linear matrix inequalities, which can guarantee the mean square stability of Markovian jumping GRNs. The novelty of this paper is that the less conservative stability criteria are obtained by utilizing Wirtinger-type integral inequality to estimate the weak infinitesimal operator of LKF. Furthermore, two illustrative examples are given to show the effectiveness of the theoretical results and the significant improvement on the existing results.