Dynamic periodic event-triggered control of stochastic complex networks with time-varying delays

This paper focuses on the exponential stabilization of stochastic complex network systems with time-varying delays. A novel dynamic periodic event-triggered control (ETC) with the graph theory and the Lyapunov-Razumikhin method is proposed. First, different from continuous ETCs, periodic sampling inherently prevents the occurrence of Zeno phenomenon. Second, compared with the traditional static ETCs, our dynamic ETC can reduce the update frequency of the controller and save communication resources by designing a proper dynamic function. Moreover, the graph theory is employed to handle the coupling relationships among nodes in complex networks and the Lyapunov-Razumikhin method is employed to address the difficulties caused by time delays in stochastic complex systems. Then, the mean-square exponential stabilization for stochastic complex network systems is obtained. Finally, a numerical example of single-link robot arm with multiple nodes is performed in a stochastic complex network system to verify the effectiveness of theoretical results.