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.
翻译:本文件审查了在矩阵加权转换网络上的多试剂系统组群共识问题;在必要和(或)充分的条件下,可以取得集群共识,并提供了集群稳定状态的定量定性;具体地说,如果首先提出有限数量网络之间的基本网络交换器,这是多试剂系统组群在转换矩阵加权网络方面达成共识的必要条件;具体地说,显示该系统的稳定状态在于与所有转换网络相对应的矩阵估值拉普拉契亚人的空域的交叉点;第二,如果利用无限数量网络之间的基本网络交换器,矩阵加权综合网络为集群共识和多试剂系统相应稳定状态的定量定性提供充足条件,利用对与转换网络相关的一体化网络的矩阵估值拉普拉比西亚人的空域分析进行空域分析;特别是,对矩阵加权转换网络下的双方共识条件进行了研究;最后提供了模拟结果,以展示理论分析。