论文标题
关于矩阵加权网络的可控性
On the Controllability of Matrix-weighted Networks
论文作者
论文摘要
这封信从图理论的角度研究了在矩阵加值网络上共识动态的可控性。与标量加权网络不同，权重矩阵等级引入了其他复杂性来表征此类网络可控子空间的维度。具体而言，我们研究了权重矩阵的确定性如何影响可控子空间的维度。在这个方向上，通过分别采用矩阵加权网络的距离分区和几乎公平的分区来提供可控子空间维度的下限和上限的图理论特征。此外，研究了此类网络的不可控制输入的结构。然后提供示例以证明理论结果。
This letter examines the controllability of consensus dynamics on matrix-weighed networks from a graph-theoretic perspective. Unlike the scalar-weighted networks, the rank of weight matrix introduces additional intricacies into characterizing the dimension of controllable subspace for such networks. Specifically, we investigate how the definiteness of weight matrices influences the dimension of the controllable subspace. In this direction, graph-theoretic characterizations of the lower and upper bounds on the dimension of the controllable subspace are provided by employing, respectively, distance partition and almost equitable partition of matrix-weighted networks. Furthermore, the structure of an uncontrollable input for such networks is examined. Examples are then provided to demonstrate the theoretical results.
