A Necessary and Sufficient Condition for Consensus of Continuous-Time Agents Over Undirected

The average consensus problem of continuous-time agents in undirected time-varying networks is studied. The network is allowed to be disconnected. A notion called infinite integral connectivity is proposed. Based on the notion, a necessary and sufficient condition for achieving con- sensus is given. That is, when the network topology is described by an undi- rected time-varying graph , the agents achieve consensus if and only if the infinite integral graph of over is connected. This crite- rion does not hold for directed networks.