TY - GEN

T1 - AR models of singular spectral matrices

AU - Anderson, Brian D.O.

AU - Deistler, Manfred

AU - Chen, Weitian

AU - Filler, Alexander

PY - 2009

Y1 - 2009

N2 - 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 D̃-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 D̃(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.

AB - 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 D̃-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 D̃(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.

UR - http://www.scopus.com/inward/record.url?scp=77950793958&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5399891

DO - 10.1109/CDC.2009.5399891

M3 - Conference contribution

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5721

EP - 5726

BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

Y2 - 15 December 2009 through 18 December 2009

ER -