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Article: Efficient positive-real balanced truncation of symmetric systems via cross-riccati equations

TitleEfficient positive-real balanced truncation of symmetric systems via cross-riccati equations
Authors
KeywordsAlternating direction implicit (ADI)
cross-Riccati equation (XRE)
Positive-real balanced truncation (PRBT)
Schur decomposition
Symmetric systems
Issue Date2008
PublisherIEEE.
Citation
Ieee Transactions On Computer-Aided Design Of Integrated Circuits And Systems, 2008, v. 27 n. 3, p. 470-480 How to Cite?
AbstractWe present a highly efficient approach for realizing a positive-real balanced truncation (PRBT) of symmetric systems. The solution of a pair of dual algebraic Riccati equations in conventional PRBT, whose cost constrains practical large-scale deployment, is reduced to the solution of one cross-Riccati equation (XRE). The cross-Riccatian nature of the solution then allows a simple construction of PRBT projection matrices, using a Schur decomposition, without actual balancing. An invariant subspace method and a modified quadratic alternating-direction-implicit iteration scheme are proposed to efficiently solve the XRE. A low-rank variant of the latter is shown to offer a remarkably fast PRBT speed over the conventional implementations. The XRE-based framework can be applied to a large class of linear passive networks, and its effectiveness is demonstrated through numerical examples. © 2008 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/57468
ISSN
2015 Impact Factor: 1.181
2015 SCImago Journal Rankings: 0.710
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWong, Nen_HK
dc.date.accessioned2010-04-12T01:37:27Z-
dc.date.available2010-04-12T01:37:27Z-
dc.date.issued2008en_HK
dc.identifier.citationIeee Transactions On Computer-Aided Design Of Integrated Circuits And Systems, 2008, v. 27 n. 3, p. 470-480en_HK
dc.identifier.issn0278-0070en_HK
dc.identifier.urihttp://hdl.handle.net/10722/57468-
dc.description.abstractWe present a highly efficient approach for realizing a positive-real balanced truncation (PRBT) of symmetric systems. The solution of a pair of dual algebraic Riccati equations in conventional PRBT, whose cost constrains practical large-scale deployment, is reduced to the solution of one cross-Riccati equation (XRE). The cross-Riccatian nature of the solution then allows a simple construction of PRBT projection matrices, using a Schur decomposition, without actual balancing. An invariant subspace method and a modified quadratic alternating-direction-implicit iteration scheme are proposed to efficiently solve the XRE. A low-rank variant of the latter is shown to offer a remarkably fast PRBT speed over the conventional implementations. The XRE-based framework can be applied to a large class of linear passive networks, and its effectiveness is demonstrated through numerical examples. © 2008 IEEE.en_HK
dc.languageengen_HK
dc.publisherIEEE.en_HK
dc.relation.ispartofIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systemsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rights©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.en_HK
dc.subjectAlternating direction implicit (ADI)en_HK
dc.subjectcross-Riccati equation (XRE)en_HK
dc.subjectPositive-real balanced truncation (PRBT)en_HK
dc.subjectSchur decompositionen_HK
dc.subjectSymmetric systemsen_HK
dc.titleEfficient positive-real balanced truncation of symmetric systems via cross-riccati equationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0278-0070&volume=27&issue=3&spage=470&epage=480&date=2008&atitle=Efficient+positive-real+balanced+truncation+of+symmetric+systems+via+cross+Riccati+equationsen_HK
dc.identifier.emailWong, N:nwong@eee.hku.hken_HK
dc.identifier.authorityWong, N=rp00190en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1109/TCAD.2008.915534en_HK
dc.identifier.scopuseid_2-s2.0-39749188160en_HK
dc.identifier.hkuros145026-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-39749188160&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume27en_HK
dc.identifier.issue3en_HK
dc.identifier.spage470en_HK
dc.identifier.epage480en_HK
dc.identifier.isiWOS:000253840500006-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridWong, N=35235551600en_HK

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