Input–output properties are studied for a linear network model with homogeneous single-input single-output subsystems. Specifically, the finite- and infinite- zero structure of a channel in the network, defined by a single external actuation and measurement, is characterized. This is done by developing a two-layer transformation for the input–output model, which expresses the zero structure in terms of the subsystem model, global network interactions (graph), and the input and output locations. This algebraic characterization then provides a means to: (1) distinguish structural properties of the input–output channel (minimum and nonminimum behavior) in terms of the network’s graph, and (2) design of the graph to shape the input–output dynamics. Similar characterizations are also briefly explored for a multiple-input multiple-output (MIMO) network model with collocated measurements and actuations.

研究了具有同质单输入单输出子系统的线性网络模型的输入-输出特性。具体来说，网络中通道的有限零和无限零结构由单个外部驱动和测量定义。这是通过为输入-输出模型开发两层转换来完成的，该模型根据子系统模型、全局网络交互（图）以及输入和输出位置表示零结构。然后，这种代数表征提供了一种方法：（1）根据网络图区分输入-输出通道的结构属性（最小和非最小行为），以及（2）设计图以塑造输入-输出动态。