Grassmann invariants, matrix pencils, and linear system properties
type: Item
instance of: scholarly article
title: Grassmann invariants, matrix pencils, and linear system properties
zbMATH Open document ID: 0877.15033
DOI: 10.1016/0024-3795(95)00590-0
author: John Leventides
author: Nicos Karcanias
published in: Linear Algebra and its Applications
publication date: 1997-11-12T00:00:00Z
review text: For general singular matrix pencil \(sF-G\) the Grassmann invariants of the pencil are introduced as the column, row Grassmann representatives \(\mathbf{g}_c(F,G), \mathbf{g}_r(F,G)^t\), and their corresponding Plücker matrices \(P_c(F,G), P_r(F,G)\), and the properties of these invariants are established. The relationship between the Grassmann-Plücker invariants of a general rational transfer function matrix and the system matrix pencil of a minimal realization is derived.
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 931906
zbMATH Keywords: singular matrix pencil
zbMATH Keywords: Plücker matrices
zbMATH Keywords: Grassmann-Plücker invariants
zbMATH Keywords: rational transfer function matrix
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: 0024-3795(95)00590-0
OpenAlex ID: W2084036924
cites work: Q3254327
cites work: Q4066911
cites work: Q5659396
cites work: The singular pencil of a linear dynamical system†
cites work: Q4750464
cites work: Matrix pencil characterization of almost ( A, Z) -invariant subspaces : A classification of geometric concepts
cites work: Grassmann invariants, almost zeros and the determinantal zero, pole assignment problems of linear multivariable systems
cites work: Q4195061
cites work: Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
cites work: Multivariable Nyquist criteria, root loci, and pole placement: A geometric viewpoint
cites work: Pole assignment of strictly proper and proper linear systems by constant output feedback
cites work: A survey of linear singular systems
cites work: Q4771383
cites work: Q4312560
cites work: Geometric theory and feedback invariants of generalized linear systems: A matrix pencil approach
cites work: Q4300058
cites work: Necessary and sufficient conditions for zero assignment by constant squaring down
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: Q4711075
cites work: Geometric state-space theory in linear multivariable control: A status report
cites work: Almost invariant subspaces: An approach to high gain feedback design--Part II: Almost conditionally invariant subspaces
cites work: Q5814388
cites work: A tutorial on the geometric analysis of linear time-invariant implicit systems
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description: scientific article; zbMATH DE number 931906