Yuan, Y and Stan, G-B and Shi, L and Barahona, M and Goncalves, J (2013) *Decentralised minimum-time consensus.* Automatica, 49. pp. 1227-1235. ISSN 0005-1098

## Abstract

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. © 2013 Elsevier Ltd. All rights reserved.

Item Type: | Article |
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Uncontrolled Keywords: | Decentralised network consensus Graph theory Laplacian matrix Minimum finite-time consensus Single node observation |

Subjects: | UNSPECIFIED |

Divisions: | Div F > Control |

Depositing User: | Cron Job |

Date Deposited: | 07 Mar 2014 11:28 |

Last Modified: | 26 Jan 2015 03:56 |

DOI: | 10.1016/j.automatica.2013.02.015 |