Discernibility of topological variations for networked LTI systems based on observed output trajectories

TL;DR

This paper investigates how to detect topological changes in networked LTI systems by analyzing output trajectories, providing necessary and sufficient conditions for discernibility based on eigenspaces and network structure considerations.

Contribution

It derives new necessary and sufficient conditions for topological discernibility in networked LTI systems, improving understanding of how network features influence detectability.

Findings

Derived a comprehensive criterion for topological discernibility.

Identified limitations of existing criteria in the literature.

Validated results through multiple illustrative examples.

Abstract

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 configuarations. 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.