The fundamental subspace sequences of matrix pencils: A Toeplitz matrix unified characterization
type: Item
instance of: scholarly article
title: The fundamental subspace sequences of matrix pencils: A Toeplitz matrix unified characterization
zbMATH Open document ID: 0919.93021
DOI: 10.1007/BF01203105
author: Helen Eliopoulou
author: Nicos Karcanias
published in: Circuits, Systems, and Signal Processing
publication date: 1999-03-14T00:00:00Z
review text: The authors introduce an alternative theoretical method for calculating the fundamental sequences of the matrix pencil \((F,G)\). These fundamental sequences are, for instance, with the right choice for \(F\) and \(G\), the elements that appear in the controllability subspace algorithm. The advantage of studying the fundamental sequences lies in the fact that one covers subspace algorithms for implicit and proper systems at the same time. These sequences of subspaces are characterized via a partition of the right null spaces of certain Toeplitz matrices. These Toeplitz matrices contain only blocks that are zero, \(F\) or \(G\), and thus are very simple to build out of the system data. Although this approach to the fundamental sequence is purely theoretical, the authors have good hope that it will be useful for (numerical) computation as well.
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 15A22
zbMATH DE Number: 1236302
zbMATH Keywords: geometrical control
zbMATH Keywords: implicit systems
zbMATH Keywords: fundamental sequences
zbMATH Keywords: matrix pencil
zbMATH Keywords: subspace algorithms
zbMATH Keywords: Toeplitz matrices
reviewed by: Hans Zwart
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01203105
OpenAlex ID: W1971725014
description: scientific article; zbMATH DE number 1236302