Consensus in Multi-Agent Systems With Coupling Delays and Switching Topology

The robustness of consensus in single integrator multi-agent systems (MAS) to coupling delays and switching topologies is investigated. It is shown that consensus is reached for arbitrarily large constant, time-varying, or distributed delays if consensus is reached without delays. This delay robustness holds under the weakest possible connectivity assumptions on the underlying graph, i.e., as long as the graph is uniformly quasi-strongly connected and switches with a dwell-time. The proof is based on a contraction argument and allows to remove technical assumptions that were used in previous publications. Moreover, the result also applies to non-scalar single integrators, an important extension toward consensus and rendezvous in higher dimensions.