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
2011 Impact Factor: 0.967
2011 SCImago Journal Rankings: 0.063
DOIhttp://dx.doi.org/10.1016/j.apnum.2004.01.013
ISI Accession Number IDWOS:000224593300005
ReferencesReferences in Scopus
DC Field
Value
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
2011 Impact Factor: 0.967
2011 SCImago Journal Rankings: 0.063
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
Author Affiliations
  1. The University of Hong Kong
  2. National University of Singapore