阈值图与余图的可控性分析
Controllability Analysis of Threshold Graphs and Cographs
摘要：
本文研究了遵循阈值图上定义的拉普拉斯动力学的线性时不变网络的可控性。在这个方向上，提出了一种算法，用于导出与这类图的拉普拉斯矩阵相关联的模态矩阵。然后，基于Popov-Belevitch-Hautus准则，提出了一种选择控制节点的方法。该过程涉及将图的节点划分为具有相同度的单元;然后从每个单元中选择一个节点。我们表明，其余的节点可以被选为控制节点，使网络可控。最后，我们考虑更广泛的一类图，即cograms，并检查其可控性。
英文摘要：
In this paper, we investigate the controllability of a linear time-invariant network following a Laplacian dynamics defined on a threshold graph. In this direction, an algorithm for deriving the modal matrix associated with the Laplacian matrix for this class of graphs is presented. Then, based on the Popov-Belevitch-Hautus criteria, a procedure for the selection of control nodes is proposed. The procedure involves partitioning the nodes of the graph into cells with the same degree; one node from each cell is then selected. We show that the remaining nodes can be chosen as the control nodes rendering the network controllable. Finally, we consider a wider class of graphs, namely cographs, and examine their controllability properties.
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