Discernibility of Topological Variations for Networked LTI Systems

In this paper, 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 [28] and [31], which require the network topology to be undirected, this condition is more general. Furthermore, the discernibility of topological variations for multi-agent systems is revisited. A new necessary and sufficient condition is established, and the indiscernible space is completely characterized. Differing from the condition provided in [31], this condition removes the requirements on the multi-agent system and has broader applicability. The effectiveness of the results is demonstrated by several examples.