Consensus of multi-agent systems with time delay based on periodic sample and event hybrid control

The consensus problem of first-order multi-agent systems with time delay is investigated. The periodic sample and event hybrid control method is applied. Specifically, each agent samples its own states periodically and decides when to transmit its sampled states to its neighbors based on certain event. The agents' distributed consensus algorithms are based on these hybrid sampled and event-triggered state measurements, which can significantly decrease the number of the controllers' updates. The Zeno behavior which is discussed in most works considering event-based consensus of multi-agent systems is excluded automatically since the span between two contiguous event-triggering time instants is not less than the sampling period. The cases of directed and undirected topologies are both considered. The obtained results improve the existing ones in the literature. A numerical simulation is provided to illustrate the effectiveness of the obtained theoretical results.