Consensus of Multiagent Systems under Communication Failure

We consider multiagent systems with cooperative interactions and study the convergence to consensus in the case of time-dependent connections, with possible communication failure. We prove a new condition ensuring consensus: we define a graph in which directed arrows corre-spond to connection functions that converge (in the weak sense) to some function with a positive integral on all intervals of the form [t, +\infty). If the graph has a node reachable from all other indices, i.e., ``globally reachable"", then the system converges to consensus. We show that this requirement generalizes some known sufficient conditions for convergence, such as Moreau's or the Persistent Excitation one. We also give a second new condition, transversal to the known ones: total connectedness of the undirected graph formed by the nonvanishing of limiting functions.