This paper examines the cluster consensus problem of multi-agent systems on matrix-weighted switching networks. Necessary and/or sufficient conditions under which cluster consensus can be achieved are obtained and quantitative characterization of the steady-state of the cluster consensus are provided as well. Specifically, if the underlying network switches amongst finite number of networks, a necessary condition for cluster consensus of multi-agent system on switching matrix-weighted networks is firstly presented, it is shown that the steady-state of the system lies in the intersection of the null space of matrix-valued Laplacians corresponding to all switching networks. Second, if the underlying network switches amongst infinite number of networks, the matrix-weighted integral network is employed to provide sufficient conditions for cluster consensus and the quantitative characterization of the corresponding steady-state of the multi-agent system, using null space analysis of matrix-valued Laplacian related of integral network associated with the switching networks. In particular, conditions for the bipartite consensus under the matrix-weighted switching networks are examined. Simulation results are finally provided to demonstrate the theoretical analysis.

中文翻译：

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矩阵加权交换网络的集群共识

本文研究了矩阵加权交换网络上多智能体系统的集群一致性问题。获得集群共识的必要和/或充分条件，并提供集群共识稳态的定量表征。具体来说，如果底层网络在有限数量的网络之间切换，首先提出了多智能体系统在切换矩阵加权网络上集群共识的必要条件，表明系统的稳态在于对应于所有交换网络的矩阵值拉普拉斯算子的零空间。其次，如果底层网络在无数个网络之间切换，采用矩阵加权积分网络为集群共识和多智能体系统相应稳态的定量表征提供充分条件，使用与切换网络相关的积分网络的矩阵值拉普拉斯相关的零空间分析. 特别地，检查了矩阵加权交换网络下的两方共识的条件。最后提供仿真结果来证明理论分析。