AR models of singular spectral matrices

Date

2009

Authors

Anderson, Brian
Deistler, Manfred
Chen, Weitian
Filler, Alexander

Journal Title

Journal ISSN

Volume Title

Publisher

Institute of Electrical and Electronics Engineers (IEEE Inc)

Abstract

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)[I m 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 W p(q), p = p 0, p 0+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.

Description

Keywords

Keywords: AR models; Auto regressive models; Auto-regressive; Column ranks; Constant matrix; Coprime; matrix; Matrix fraction description; Spectral matrices; Submatrix; Transfer function matrix; Equivalence classes; Set theory; Matrix algebra

Citation

Source

Proceedings of IEEE Conference on Decision and Control and Chinese Control Conference 2009

Type

Conference paper

Book Title

Entity type

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2037-12-31