A combinatorial necessary and sufficient condition for cluster consensus

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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.
Original languageEnglish
Pages (from-to)611-616
Number of pages6
JournalNeurocomputing
Volume216
Early online date11 Aug 2016
DOIs
Publication statusPublished - 5 Dec 2016

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