Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observability through matrix-weighted graph   Observability of an array of identical LTI systems with incommensurable
output matrices is studied, where an array is called observable when
identically zero relative outputs imply synchronized solutions for the
individual systems. It is shown that the observability of an array is
equivalent to the connectivity of its interconnection graph, whose edges are
assigned matrix weights. The interconnection graph is studied by means of a
collection of simpler graphs, each of which is associated to an eigenvalue of
the system matrix of individual dynamics. It is reported that the
interconnection graph is connected if and only if no member of this collection
is disconnected. Moreover, to better understand the relative behavior of
distant units, pairwise observability which concerns with the synchronization
of a certain pair of individual systems in the array is studied. This milder
version of observability is shown to be closely related to certain connectivity
properties of the interconnection graph as well. Pairwise observability is also
analyzed using the circuit theoretic tool effective conductance. The
observability of a certain pair of units is proved to be equivalent to the
nonsingularity of the (matrix-valued) effective conductance between the
associated pair of nodes of a resistive network (with matrix-valued parameters)
whose node admittance matrix is the Laplacian of the array's interconnection
graph.

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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom