Complete parametric approach for eigenstructure assignment in a class of second-order linear systems
type: Item
instance of: scholarly article
title: Complete parametric approach for eigenstructure assignment in a class of second-order linear systems
zbMATH Open document ID: 1009.93036
DOI: 10.1016/S0005-1098(01)00251-5
author: Guangren Duan
author: Guo-Ping Liu
published in: Automatica
publication date: 2002-09-05T00:00:00Z
review text: This paper considers eigenstructure assignment via proportional-plus-derivative feedback control in a class of second-order linear systems in the form of \(\ddot q- A\dot q- Cq= Bu\). Under the controllability condition of the matrix pair \([A,B]\), simple complete parametric expressions for both the closed-loop eigenvector matrices and the feedback gain matrices are established in terms of the closed-loop eigenvalues and a group of parameter vectors. Both the closed-loop eigenvalues and the group of parameters can be properly chosen to produce a closed-loop system with some additional desired specifications. The main computations involved are the Smith form reductions of two polynomial matrices, or two sets of singular value decompositions when the closed-loop eigenvalues are known a priori. A third-order illustrative example is presented.
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93B60
zbMATH DE Number: 1797047
zbMATH Keywords: second-order systems
zbMATH Keywords: eigenstructure assignment
zbMATH Keywords: proportional-plus-derivative controllers
zbMATH Keywords: closed-loop eigenvector
zbMATH Keywords: closed-loop eigenvalues
zbMATH Keywords: Smith form reductions
zbMATH Keywords: singular value decompositions
reviewed by: Petko Hr. Petkov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1797047