In this note, we consider networks that are governed by external controls. The internal nodes of the network are composed of structured linear dynamic systems with a single incoming state vertex and a single outgoing state vertex. Combining the network graph with the node graphs provides with a global graph that will allow the study of the structural controllability of the global system. We give necessary and sufficient controllability conditions for the global system, with respect to the controllability of the nodes and to the properties of the network graph. The conditions are expressed in terms of an auxiliary graph that has the same size as the network graph, but takes into account important features of the node graphs. Besides its interest in terms of insight in the controllability of networks with dynamical nodes, this approach is also much more efficient computationally than a direct checking of the controllability of the global system.

中文翻译：

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非等温轴向分散管式反应器平衡分布存在性分析


在本说明中，我们考虑受外部控制控制的网络。网络的内部节点由具有单个输入状态顶点和单个输出状态顶点的结构化线性动态系统组成。将网络图与节点图相结合提供了一个全局图，可以研究全局系统的结构可控性。我们针对节点的可控性和网络图的属性给出了全局系统的充分必要的可控性条件。条件用与网络图大小相同的辅助图来表示，但考虑了节点图的重要特征。除了深入了解具有动态节点的网络的可控性之外，这种方法在计算上也比直接检查全局系统的可控性要高效得多。