In this paper we investigate the herdability property, namely the capability of a system to be driven towards the (interior of the) positive orthant, for linear time-invariant state space models. Herdability of certain matrix pairs $(A,B)$, where $A$ is the adjacency matrix of a multi-agent network, and $B$ a selection matrix that singles out a subset of the agents (the “network leaders”), is explored. The cases when the graph associated with $A$, $\mathcal{G}\left(A\right)$, is directed and clustering balanced (in particular, structurally balanced), or it has a tree topology and there is a single leader, are investigated.

中文翻译：

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具有特殊拓扑结构的线性时不变系统的可群性

在本文中，我们研究了线性时不变状态空间模型的可群性特性，即系统被驱动到正向（的内部）的能力。某些矩阵对的群聚性$(\mathrm{一种},乙)$， 在哪里$\mathrm{一种}$是多智能体网络的邻接矩阵，并且$乙$探索了一个选择矩阵，该矩阵挑选出代理人的一个子集（“网络领导者”）。图关联的情况$\mathrm{一种}$,$\mathcal{G}\left(\mathrm{一种}\right)$，是有向的并且集群是平衡的（特别是在结构上是平衡的），或者它具有树形拓扑结构并且只有一个领导者，都被研究过。