Synchronization in Networks of Linearly Coupled Dynamical Systems via Event-Triggered Diffusions

In this paper, we utilize event-triggered coupling configurations to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes and their neighborhood and the next observation time is triggered by the proposed criteria based on the local neighborhood information as well. Two scenarios are considered: 1) continuous monitoring, in which each node can observe its neighborhood's instantaneous states and 2) discrete monitoring, in which each node can obtain only its neighborhood's states at the same time point when the coupling term is triggered. In both the cases, we prove that if the system with persistent coupling can synchronize, then these event-triggered coupling strategies can synchronize the system too.