Reference : Decentralised minimum-time consensus
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Decentralised minimum-time consensus
Yuan, Ye mailto []
Stan, Guy-Bart mailto []
Shi, Ling mailto []
Barahona, Mauricio mailto []
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Pergamon Press - An Imprint of Elsevier Science
Yes (verified by ORBilu)
United Kingdom
[en] Decentralised network consensus ; Minimum finite-time consensus ; Single node observation ; Laplacian matrix ; Graph theory
[en] We consider the discrete-time dynamics of a network of agents that exchange information according to
a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically.
We present a fully decentralised algorithm that allows any agent to compute the final consensus value of
the whole network in finite time using the minimum number of successive values of its own state history.
We show that the minimum number of steps is related to a Jordan block decomposition of the network
dynamics, and present an algorithm to compute the final consensus value in the minimum number of
steps by checking a rank condition of a Hankel matrix of local observations. Furthermore, we prove that
the minimum number of steps is related to graph theoretical notions that can be directly computed from
the Laplacian matrix of the graph and from the minimum external equitable partition.

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