Discernibility of Topological Variations for Networked LTI Systems

In this article, the discernibility of topological variations for networked linear time-invariant (LTI) systems is investigated, where the network topology is general, and the nodes have identical higher dimensional dynamics. A necessary and sufficient condition on the discernibility is derived, revealing how the topological variations, node-system dynamics, and inner interactions altogether affect the discernibility of the network. Compared with the existing conditions in (Patil et al., 2019) and (Roy et al., 2020), which require the network topology to be undirected, this condition is more general. Furthermore, the discernibility of topological variations for multiagent systems is revisited. A new necessary and sufficient condition is established, and the indiscernible space is completely characterized. Differing from the condition provided in (Roy et al., 2020), this condition removes the requirements on the multiagent system and has broader applicability. The effectiveness of the results is demonstrated by several examples.