In this paper, the possibility of detecting topological variations by observing output trajectories from networked linear time-invariant systems is investigated, where the network topology can be general, but the nodes have identical higher-dimensional dynamics. A necessary and sufficient condition on the discernibility of topological variations is derived, in terms of the eigenspaces of the original and the modified network configurations. By taking the specific network structures into consideration, some lower-dimensional conditions are derived, which reveal how the network topologies, sensor locations, node-system dynamics and output, as well as inner interactions altogether affect the discernibility. Furthermore, the output discernibility of topological changes for networked multi-agent systems is revisited, showing that some criterion reported in the literature does not hold. Consequently, a modified necessary and sufficient condition is established. The effectiveness of the results is demonstrated through several examples.

中文翻译：

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基于观察到的输出轨迹的网络 LTI 系统拓扑变化的辨别力

在本文中，研究了通过观察网络线性时不变系统的输出轨迹来检测拓扑变化的可能性，其中网络拓扑可以是通用的，但节点具有相同的高维动态。根据原始网络配置和修改后的网络配置的特征空间，导出了拓扑变化可辨别性的充分必要条件。通过考虑特定的网络结构，推导了一些低维条件，这些条件揭示了网络拓扑、传感器位置、节点系统动力学和输出以及内部相互作用如何共同影响可辨别性。此外，重新审视了网络多智能体系统拓扑变化的输出可辨别性，表明文献中报告的某些标准不成立。因此，修改后的充分必要条件成立。通过几个例子证明了结果的有效性。