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 graph G(t), the agents achieve consensus if and only if the infinite integral graph of G(t) over [0,∞) is connected. This criterion does not hold for directed networks.
Published in:
Automatic Control, IEEE Transactions on
(Volume:56
,
Issue:
8
)
Date of Publication: Aug. 2011