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
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Source
Proceedings of IEEE Conference on Decision and Control and Chinese Control Conference 2009
Type
Conference paper
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2037-12-31