A combinatorial necessary and sufficient condition for cluster consensus

作者：Shang Yilun^*

来源：Neurocomputing, 2016, 216: 611-616.

DOI：10.1016/j.neucorn.2016.08.025

• Cluster consensus
• Multi-agent system
• Linear switched System
• Cooperative control

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.

• 出版日期2016-12-5
• 单位同济大学