A combinatorial necessary and sufficient condition for cluster consensus

Shang, Yilun (2016) A combinatorial necessary and sufficient condition for cluster consensus. Neurocomputing, 216. pp. 611-616. ISSN 0925-2312

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Official URL: http://dx.doi.org/10.1016/j.neucom.2016.08.025

Abstract

In this letter, cluster consensus of discrete-time linear multi-agent systems is investigated. A set of stochastic matrices P is said to be a cluster consensus set if the system achieves cluster consensus for any initial state and any sequence of matrices taken from P. By introducing a cluster ergodicity coefficient, we present an equivalence relation between a range of characterization of cluster consensus set under some mild conditions including the widely adopted inter-cluster common influence. We obtain a combinatorial necessary and sufficient condition for a compact set P to be a cluster consensus set. This combinatorial condition is an extension of the avoiding set condition for global consensus, and can be easily checked by an elementary routine. As a byproduct, our result unveils that the cluster-spanning tree condition is not only sufficient but necessary in some sense for cluster consensus problems.

Item Type: Article
Uncontrolled Keywords: Cluster consensus, multi-agent system, linear switched system, cooperative control
Subjects: G100 Mathematics
G400 Computer Science
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Paul Burns
Date Deposited: 08 Nov 2018 14:21
Last Modified: 11 Oct 2019 18:04
URI: http://nrl.northumbria.ac.uk/id/eprint/36565

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