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M. Deistler, Brian Anderson, W. Chen, A. Filler:
"AR Models of Singular Spectral Matrices";
in: "Proceedings of IEEE CDC 2009", IEEE, 2009, (invited), ISBN: 978-1-4244-3871-6, Paper ID ThC14.1, 6 pages.

This paper deals with autoregressive models of

singular spectra. The starting point is the assumption that there

is available a transfer function matrix W(q) expressible in the

form D��1(q)B for some tall constant matrix B of full column

rank and with the determinantal zeros of D(q) all stable. It

is shown that, even if this matrix fraction representation of

W(q) is not coprime, W(q) has a coprime matrix fraction

description of the form ~D��1(q)[Im 0]T . It is also shown how to

characterize the equivalence class of all autoregressive matrix

fraction descriptions of W(q), and how canonical representatives

can be obtained. A canonical representative can be obtained with

a minimal set of row degrees for the submatrix of ~D (q) obtained

by deleting the first m rows. The paper also considers singular

autoregressive descriptions of nested sequences of Wp(q); p =

p0; p0 +1; : : : ; where p denotes the number of rows, and shows

that these canonical descriptions are nested, and contain a

number of parameters growing linearly with p.

http://dx.doi.org/10.1109/CDC.2009.5399891

http://publik.tuwien.ac.at/files/PubDat_178518.pdf