Interlacing inequalities and control theory
type: Item
instance of: scholarly article
title: Interlacing inequalities and control theory
zbMATH Open document ID: 0673.93025
DOI: 10.1016/0024-3795(88)90140-1
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: As it is well known the controllability indices and the invariant factors of a matrix pair (A,B) form a complete system of invariants for the state-feedback equivalence or block similarity. In this paper the following problem is solved: given an \(n\times n\) matrix A over an arbitrary field, under what conditions does there exist an \(n\times m\) matrix B such that the pair (A,B) is in a prescribed state-feedback equivalence class? The solution of this problem includes a characterization of the possible controllability indices of all controllable pairs (A,B) as B runs over the set of \(m\times n\) matrices. The solution of the first problem together with a result in an earlier paper of the author [ibid. 87, 113-146 (1987; Zbl 0632.15003)] is used to provide a new proof of the so-called Sá-Thompson interlacing inequalities for invariant factors [\textit{E. Marques de Sá}, ibid. 24, 33-50 (1979; Zbl 0395.15009); \textit{R. C. Thompson}, ibid. 24, 1-31 (1979; Zbl 0395.15003)], which characterize the matrices belonging to a prescribed similarity class and having a prescribed principal submatrix.
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 4102905
zbMATH Keywords: interlacing inequalities
zbMATH Keywords: majorization
zbMATH Keywords: controllability indices
zbMATH Keywords: invariant factors
zbMATH Keywords: state-feedback equivalence class
author: Ion Zaballa
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90140-1
OpenAlex ID: W2088876089
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Wikidata QID: Q126351650
description: scientific article; zbMATH DE number 4102905