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

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3 Author(s)
Li Cao ; Dept. of Comput. Sci. & Technol., East China Normal Univ., Shanghai, China ; Yufan Zheng ; Qing Zhou

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

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