Synchronization for stochastic Lévy noise systems on a time-varying multi-weights network via delay intermittent control

In previous papers, either the time-varying coupling structure or multi-weights have been considered into networks. However, few scholars have paid attention to networks with both time-varying coupling structure and multi-weights. In this paper, we formulate and probe stochastic Lévy noise delayed systems on a time-varying multi-weights network (SLDSTN) for the first time. In order to solve the synchronization problem of SLDSTN, we design a novel class of delay intermittent control. Different from previous intermittent control based on current state, delay intermittent control is based on past state. Then, by means of Lyapunov method, graph theory and some techniques of inequalities, sufficient conditions for exponential synchronization in mean square of SLDSTN are proposed. Therein, we relax the condition of processing the time-varying coupling term successfully. Furthermore, for presenting the superiorities of delay intermittent control, delay feedback control and aperiodically intermittent control also are applied to solve the synchronization problem of SLDSTN. To demonstrate the effectiveness of the theoretical results, a class of single-link robot arms is considered as a practical application. Finally, some numerical simulations are provided.