The solution to the matrix equation \(AV+BW=EVJ+R\).
type: Item
instance of: scholarly article
title: The solution to the matrix equation \(AV+BW=EVJ+R\).
zbMATH Open document ID: 1065.15015
author: Guangren Duan
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: The generalized Sylvester matrix equation \(AV+BW=EVJ\) finds application in many problems in linear systems theory. The matrices \(A\), \(E\), \(B\), \(J\), \(V\) and \(W\) are respectively \(n\times n\), \(n\times n\), \(n\times r\), \(p\times p\), \(n\times p\) and \(r\times p\); \(J\) is Jordan and \(V\), \(W\) are to be determined. The author deals with the corresponding inhomogeneous equation \(AV+BW=EVJ+R\) encountered when dealing with complicated linear systems; the matrix \(R\) is \(n\times p\). He obtains the general parametric solution to this equation based on the Smith form reduction of the matrix \([A-sE\;B]\); it is not required the eigenvalues of \(J\) to be known. The proposed solution is illustrated by an example.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 2140804
zbMATH Keywords: generalized Sylvester matrix equation
zbMATH Keywords: parametric solution
zbMATH Keywords: \(R\)-controllability
zbMATH Keywords: Smith form reduction
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: j.aml.2003.05.012
OpenAlex ID: W2051997016
cites work: Solution to matrix equation \(AV + BW = EVF\) and eigenstructure assignment for descriptor systems
cites work: Solutions of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems
cites work: Eigenstructure assignment in descriptor systems via output feedback: A new complete parametric approach
cites work: Eigenstructure assignment in descriptor systems
cites work: Geometric structure and feedback in singular systems
cites work: Singular control systems
cites work: Control of linear systems with regulation and input constraints
cites work: Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - a survey and some new results
cites work: Robust fault detection using Luenberger-type unknown input observers-a parametric approach
cites work: On the solution to the Sylvester matrix equation AV+BW=EVF
cites work: Complete parametric approach for eigenstructure assignment in a class of second-order linear systems
cites work: Robust eigenstructure assignment via dynamical compensators
cites work: Robust pole assignment in descriptor linear systems via state feedback
DOI: 10.1016/J.AML.2003.05.012
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description: scientific article; zbMATH DE number 2140804