Event-based agreement protocols for complex networks with time delays under pinning control

Most pinning synchronization schemes for complex networks with or without time delays reported in the literature require continuous state measurements and control updates, which are not suitable for implementation on digital platforms. In this paper, we first establish some pinning synchronization criteria for complex networks modeled by directed graphs with both internal and coupling delays based on an event-triggered mechanism. We also propose the design method for control gains under some mild assumptions. The piecewise constant nature of control law can help reduce the number of updates significantly, thereby saving energy resources. Moreover, by obtaining an explicit lower bound on the inter-event time interval, we prove that Zeno behavior does not exist in the evolution of each node of the complex network. At last, simulations are provided which verify the effectiveness of the proposed controllers.