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Article: A numerically reliable solution for the squaring-down problem in system design
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TitleA numerically reliable solution for the squaring-down problem in system design
 
AuthorsChu, D2
Hung, YS1
 
KeywordsCompensator
Infinite zero
Invariant zero
Orthogonal transformation
Squaring-down
 
Issue Date2004
 
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/apnum
 
CitationApplied Numerical Mathematics, 2004, v. 51 n. 2-3, p. 221-241 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.apnum.2004.01.013
 
AbstractIn this paper, matrix pencil theory is used to study the squaring-down problem where a linear time-invariant system with an unequal number of inputs and outputs is turned into an invertible square system with an equal number of inputs and outputs. Both static and dynamic compensators are considered for squaring down. In the case of static compensation, the infinite-zero structure of the original system is preserved after squaring down. In the case of dynamic compensation, key system properties including stabilizability, detectability and the infinite-zero structure of the original system are also preserved after squaring down. Furthermore, one can additionally assign the invariant zeros induced by squaring down to the open left half plane, provided that the original system is stabilizable and detectable. This means that squaring down by dynamic compensation preserves minimum phaseness as well. The preservation of these system properties is highly desirable for subsequent feedback design of the squared-down system. Unlike existing squaring-down methods which do not address the issue of numerical properties, our solution is based on a condensed form derived using only orthogonal transformations which are numerically stable. Explicit formulas which can be implemented in a numerically reliable manner are given for determining the squaring-down compensators. Examples are presented to illustrate the numerical superiority of the proposed method. © 2004 IMACS. Publishesd by Elsevier B.V. All Rights reserved.
 
ISSN0168-9274
2013 Impact Factor: 1.036
2013 SCImago Journal Rankings: 1.163
 
DOIhttp://dx.doi.org/10.1016/j.apnum.2004.01.013
 
ISI Accession Number IDWOS:000224593300005
 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorChu, D
 
dc.contributor.authorHung, YS
 
dc.date.accessioned2010-09-06T06:53:37Z
 
dc.date.available2010-09-06T06:53:37Z
 
dc.date.issued2004
 
dc.description.abstractIn this paper, matrix pencil theory is used to study the squaring-down problem where a linear time-invariant system with an unequal number of inputs and outputs is turned into an invertible square system with an equal number of inputs and outputs. Both static and dynamic compensators are considered for squaring down. In the case of static compensation, the infinite-zero structure of the original system is preserved after squaring down. In the case of dynamic compensation, key system properties including stabilizability, detectability and the infinite-zero structure of the original system are also preserved after squaring down. Furthermore, one can additionally assign the invariant zeros induced by squaring down to the open left half plane, provided that the original system is stabilizable and detectable. This means that squaring down by dynamic compensation preserves minimum phaseness as well. The preservation of these system properties is highly desirable for subsequent feedback design of the squared-down system. Unlike existing squaring-down methods which do not address the issue of numerical properties, our solution is based on a condensed form derived using only orthogonal transformations which are numerically stable. Explicit formulas which can be implemented in a numerically reliable manner are given for determining the squaring-down compensators. Examples are presented to illustrate the numerical superiority of the proposed method. © 2004 IMACS. Publishesd by Elsevier B.V. All Rights reserved.
 
dc.description.naturelink_to_subscribed_fulltext
 
dc.identifier.citationApplied Numerical Mathematics, 2004, v. 51 n. 2-3, p. 221-241 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.apnum.2004.01.013
 
dc.identifier.doihttp://dx.doi.org/10.1016/j.apnum.2004.01.013
 
dc.identifier.epage241
 
dc.identifier.hkuros101317
 
dc.identifier.isiWOS:000224593300005
 
dc.identifier.issn0168-9274
2013 Impact Factor: 1.036
2013 SCImago Journal Rankings: 1.163
 
dc.identifier.issue2-3
 
dc.identifier.openurl
 
dc.identifier.scopuseid_2-s2.0-5144222420
 
dc.identifier.spage221
 
dc.identifier.urihttp://hdl.handle.net/10722/73669
 
dc.identifier.volume51
 
dc.languageeng
 
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/apnum
 
dc.publisher.placeNetherlands
 
dc.relation.ispartofApplied Numerical Mathematics
 
dc.relation.referencesReferences in Scopus
 
dc.rightsApplied Numerical Mathematics. Copyright © Elsevier BV.
 
dc.subjectCompensator
 
dc.subjectInfinite zero
 
dc.subjectInvariant zero
 
dc.subjectOrthogonal transformation
 
dc.subjectSquaring-down
 
dc.titleA numerically reliable solution for the squaring-down problem in system design
 
dc.typeArticle
 
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Author Affiliations
  1. The University of Hong Kong
  2. National University of Singapore