论文标题
通过平衡集来表征在签名的矩阵加权网络上的双方共识
Characterizing Bipartite Consensus on Signed Matrix-Weighted Networks via Balancing Set
论文作者
论文摘要
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.为了重新建立网络结构与双方共识解决方案之间的关系，引入了非平衡平衡集，这是一组边缘的边缘，其符号可以将结构不平衡的网络转换为结构平衡的网络，并且与此组合中的边缘相关的重量矩阵具有非底片的空位。我们表明，在基质加权网络上两分性共识的必要条件和/或足够的条件可以以非平衡平衡集的独特性为特征，而相关的非平衡空间对基质稳态网络稳态的非平凡相交的贡献。此外，对于具有阳性阴性树的基质加权网络，使用非平衡平衡集获得了两分化共识的必要条件。提供了模拟示例以证明理论结果。
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.
