Fundamental properties of the manifold of singular and regular linear systems
type: Item
instance of: scholarly article
title: Fundamental properties of the manifold of singular and regular linear systems
zbMATH Open document ID: 0611.93011
DOI: 10.1016/0022-247X(86)90220-9
author: J. Daniel Cobb
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: This paper constructs a real analytic manifold L of equivalence classes of systems of the form \(Ex'=Ax+Bu\), \(y=Cx\). Here E, A, B, C are constant matrices, E, A are square, and the pencil zE-A is regular. It is shown that L is the completion, with respect to solutions of the set of regular state space systems, that is those with E nonsingular. Other geometric and analytic properties of L are established, including genericity of the regular systems.
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3989185
zbMATH Keywords: singular system
zbMATH Keywords: equivalence classes
zbMATH Keywords: completion
zbMATH Keywords: geometric and analytic properties
zbMATH Keywords: time-invariant
reviewed by: Stephen L. Campbell
MaRDI profile type: Publication
cites work: Q3902963
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full work available at URL: 0022-247x(86)90220-9
OpenAlex ID: W2152839295
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description: scientific article; zbMATH DE number 3989185