Title :
A Necessary and Sufficient Condition for Consensus of Continuous-Time Agents Over Undirected Time-Varying Networks
Author :
Cao, Li ; Zheng, Yufan ; Zhou, Qing
Author_Institution :
Dept. of Comput. Sci. & Technol., East China Normal Univ., Shanghai, China
Abstract :
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.
Keywords :
continuous time systems; graph theory; integral equations; multi-agent systems; network theory (graphs); time-varying systems; continuous-time agents; infinite integral connectivity; infinite integral graph; network topology; undirected time-varying graph; undirected time-varying networks; Communication networks; Laplace equations; Mobile communication; Multiagent systems; Network topology; Topology; Trajectory; Consensus; disconnected networks; integral connectivity; stability analysis; time-varying networks;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2157393
