Averaging approach for consensus of fast switching multi-agent networks with delayed communications

This paper investigates the consensus problem of networked nonlinear agents with fast switched topologies. The communications between agents are assumed to be directed and delayed. To reflect a practical scenario with fast-varying topologies, the network is assumed to be switched within a finite set of topologies. In order to construct sufficient criteria for consensus, the classical Lyapunov functional stability theory and the averaging approach are utilised, and a relation between the consensus criteria for the time-averaged network and the studied network is hereby unveiled. Our theory manifests that, the consensus of the time-averaged network may induce consensus of the original switched network if a high-enough switching frequency is applied. It is remarkable to point out that that consensus may also be achievable even when all networks are disconnected. Numerical simulations are also carried out for demonstration and verification purpose.