二部图
数学
有符号图
独特性
离散数学
组合数学
等价(形式语言)
集合(抽象数据类型)
基质(化学分析)
图形
计算机科学
数学分析
材料科学
复合材料
程序设计语言
作者
Chongzhi Wang,Lulu Pan,Haibin Shao,Dewei Li,Yugeng Xi
出处
期刊:Automatica
[Elsevier]
日期:2022-04-08
卷期号:141: 110237-110237
被引量:7
标识
DOI:10.1016/j.automatica.2022.110237
摘要
In contrast with the scalar-weighted networks, where bipartite consensus can be achieved if and only if the underlying signed network is structurally balanced, the structural balance property is no longer a graph-theoretic equivalence to the bipartite consensus in the case of signed matrix-weighted networks. To re-establish the relationship between the network structure and the bipartite consensus solution, the non-trivial balancing set is introduced which is a set of edges whose sign negation can transform a structurally imbalanced network into a structurally balanced one and the weight matrices associated with edges in this set have a non-trivial intersection of null spaces. We show that necessary and/or sufficient conditions for bipartite consensus on matrix-weighted networks can be characterized by the uniqueness of the non-trivial balancing set, while the contribution of the associated non-trivial intersection of null spaces to the steady-state of the matrix-weighted network is examined. Moreover, for matrix-weighted networks with a positive–negative spanning tree, necessary and sufficient condition for bipartite consensus using the non-trivial balancing set is obtained. Simulation examples are provided to demonstrate the theoretical results.
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