Periodically intermittent control for stochastic nonlinear delay systems with dynamic event-triggered mechanism

In this article, the mean-square exponential stability of the stochastic nonlinear delay systems with dynamic event-triggered mechanism under periodically intermittent control scheme is concerned. First, to avoid Zeno behavior, the triggered mechanism contains with a fixed positive lower bound for the inter-execution time is constructed. Then, an auxiliary system with dynamic event-triggering mechanism under continuous control is introduced. Combining the Lyapunov theorem with Halanay inequality, the sufficient conditions and the mean-square exponential stability of the auxiliary system are obtained. In addition, by using the comparison theorem, the exponential stability of the system under intermittent control is also proved. Meanwhile, the lower bound of the duty cycle for a fixed period under intermittent controller is obtained. Furthermore, we apply the theoretical results to the consensus of stochastic nonlinear delay networked multi-agent systems (MASs) with dynamic event-triggered mechanism. Finally, numerical examples are given to verify the effectiveness of the proposed methods.