Averaging method for consensus of fast switching multi-agent networks with communication delay

This work investigates the consensus problem of a group of nonlinear agents over a fast-switching network. The communications between agents are bidirectional and time delay exists. The topology, which specifies the communications, is assumed to be switched within a finite set of topologies, reflecting a practical fast-varying network environment. Based on the Lyapunov functional stability theory and the averaging technique, a relation between the consensus condition for the time-averaged network and the studied network is established. It reveals that, when the switching frequency is high enough, the consensus of the time-averaged network induces the consensus of its counterpart. This result has been verified and illustrated by numerical simulations. It is also interesting to note that consensus is possible even when all networks are disconnected.