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Article: Solving quadratic distance problems: An LMI-based approach

TitleSolving quadratic distance problems: An LMI-based approach
Authors
KeywordsDistance Problems
Homogeneous Forms
Linear Matrix Inequalities (Lmis)
Optimization
Issue Date2003
Citation
Ieee Transactions On Automatic Control, 2003, v. 48 n. 2, p. 200-212 How to Cite?
AbstractThe computation of the minimum distance of a point to a surface in a finite-dimensional space is a key issue in several system analysis and control problems. This paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality (LMI) techniques. Exploiting a suitable representation of homogeneous forms, a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one-parameter family of LMI optimization problems. Several properties of the proposed technique are discussed. In particular, tightness of the lower bound is investigated, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori. Extensive numerical simulations are reported showing promising performances of the proposed method.
Persistent Identifierhttp://hdl.handle.net/10722/155183
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.contributor.authorGarulli, Aen_US
dc.contributor.authorTesi, Aen_US
dc.contributor.authorVicino, Aen_US
dc.date.accessioned2012-08-08T08:32:13Z-
dc.date.available2012-08-08T08:32:13Z-
dc.date.issued2003en_US
dc.identifier.citationIeee Transactions On Automatic Control, 2003, v. 48 n. 2, p. 200-212en_US
dc.identifier.issn0018-9286en_US
dc.identifier.urihttp://hdl.handle.net/10722/155183-
dc.description.abstractThe computation of the minimum distance of a point to a surface in a finite-dimensional space is a key issue in several system analysis and control problems. This paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality (LMI) techniques. Exploiting a suitable representation of homogeneous forms, a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one-parameter family of LMI optimization problems. Several properties of the proposed technique are discussed. In particular, tightness of the lower bound is investigated, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori. Extensive numerical simulations are reported showing promising performances of the proposed method.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Transactions on Automatic Controlen_US
dc.subjectDistance Problemsen_US
dc.subjectHomogeneous Formsen_US
dc.subjectLinear Matrix Inequalities (Lmis)en_US
dc.subjectOptimizationen_US
dc.titleSolving quadratic distance problems: An LMI-based approachen_US
dc.typeArticleen_US
dc.identifier.emailChesi, G:chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1109/TAC.2002.808465en_US
dc.identifier.scopuseid_2-s2.0-0037291895en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0037291895&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume48en_US
dc.identifier.issue2en_US
dc.identifier.spage200en_US
dc.identifier.epage212en_US
dc.identifier.isiWOS:000181099700002-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridChesi, G=7006328614en_US
dc.identifier.scopusauthoridGarulli, A=7003697493en_US
dc.identifier.scopusauthoridTesi, A=7007124648en_US
dc.identifier.scopusauthoridVicino, A=7006250298en_US
dc.identifier.citeulike7787860-

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