Second-order consensus in time-delayed networks based on periodic edge-event driven control

The second-order consensus problems in multi-agent systems with undirected topologies and time-invariant delays are considered in this paper. The time-delay robustness of a consensus protocol based on periodic edge-event driven control is investigated, and the studied protocol can largely reduce the communication and controller-updating costs. The relationship between time delays and event-detecting period is characterized. By Lyapunov methods, it is shown that the protocol can solve state consensus problems when the interaction topology is connected, and the system does not exhibit Zeno behavior. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.