Stabilization of stochastic Markovian switching systems on networks with multilinks based on aperiodically intermittent control: A new differential inequality technique

In this paper, the stabilization problem of stochastic Markovian switching systems on networks with multilinks and time-varying delays (SMNMT) is investigated via aperiodically intermittent control. At first, a new differential inequality is established for SMNMT, which relaxes the conditions of time-varying delays compared with existing literature. Different from previous approaches of studying multilinks systems, new differential inequality technique combined with graph theory and Lyapunov method is adopted, based on which two types of sufficient conditions are derived to ensure the stability of SMNMT. The topological structure of multilinks systems on networks, stochastic perturbation, the transition rate of Markov chain, and intermittent control has a great impact on these developed conditions. The theoretical results are applied to stochastic Markovian switching oscillators networks with multilinks (SMONM), and a stabilization criterion of SMONM is derived as well. Finally, a numerical example is shown to illustrate the feasibility of our theoretical results.