A Necessary and Sufficient Condition for Consensus of Continuous-Time Agents Over Undirected Time-Varying Networks
Li Cao, Yufan Zheng, Qing Zhou · IEEE Transactions on Automatic Control · 2011
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 consensus is given. That is, when the network topology is described by an undirected time-varying graphG(t), the agents achieve consensus if and only if the infinite integral graph ofG(t) over [0,∞) is connected. This criterion does not hold for directed networks.