Abstract
This study focuses on the observability of second-order linear time invariant (LTI) systems with incommensurable output matrices through a matrix-weighted graph. Here, the observability of such systems refers to that the relative outputs have synchronized solutions for the identical LTI systems. Compared with most of existing results, relying on scalar networks (i.e., the weight of edges is a constant), this study investigates the observability in a matrix-weight-based network. Some necessary and sufficient conditions for the observability have been obtained by the space analysis, spectral analysis and matrix decomposition, respectively. Moreover, the relationship between the observability and the connectivity of its interconnection graph is also discussed. Examples and simulations are shown to verify the theoretical results.
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