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Conference Paper: Characterizing the positive polynomials which are not SOS

TitleCharacterizing the positive polynomials which are not SOS
Authors
Chesi, G
KeywordsHilbert's 17th problem
LMI
Optimization in control
Positive polynomial
SOS
Issue Date2005
PublisherIEEE. The Journal's web site is located at http://www.ieeecss.org
Citation
Proceedings Of The 44Th Ieee Conference On Decision And Control, And The European Control Conference, Cdc-Ecc '05, 2005, v. 2005, p. 1642-1647 How to Cite?
DOI: http://dx.doi.org/10.1109/CDC.2005.1582394
AbstractSeveral analysis and synthesis tools in control systems are based on polynomial sum of squares (SOS) relaxations. However, almost nothing is known about the gap existing between positive polynomials and SOS of polynomials. This paper investigates such a gap proposing a matrix characterization of PNS, that is homogeneous forms that are not SOS. In particular, it is shown that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parameterization of the set of PNS is introduced. © 2005 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/54062
ISSN
0743-1546
2023 SCImago Journal Rankings: 0.721
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.date.accessioned2009-04-03T07:35:45Z-
dc.date.available2009-04-03T07:35:45Z-
dc.date.issued2005en_HK
dc.identifier.citationProceedings Of The 44Th Ieee Conference On Decision And Control, And The European Control Conference, Cdc-Ecc '05, 2005, v. 2005, p. 1642-1647en_HK
dc.identifier.issn0743-1546en_HK
dc.identifier.urihttp://hdl.handle.net/10722/54062-
dc.description.abstractSeveral analysis and synthesis tools in control systems are based on polynomial sum of squares (SOS) relaxations. However, almost nothing is known about the gap existing between positive polynomials and SOS of polynomials. This paper investigates such a gap proposing a matrix characterization of PNS, that is homogeneous forms that are not SOS. In particular, it is shown that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parameterization of the set of PNS is introduced. © 2005 IEEE.en_HK
dc.languageengen_HK
dc.publisherIEEE. The Journal's web site is located at http://www.ieeecss.orgen_HK
dc.relation.ispartofProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05en_HK
dc.rights©2005 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.-
dc.subjectHilbert's 17th problemen_HK
dc.subjectLMIen_HK
dc.subjectOptimization in controlen_HK
dc.subjectPositive polynomialen_HK
dc.subjectSOSen_HK
dc.titleCharacterizing the positive polynomials which are not SOSen_HK
dc.typeConference_Paperen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0743-1546&volume=&spage=1642&epage=1647&date=2005&atitle=Characterizing+the+positive+polynomials+which+are+not+SOSen_HK
dc.identifier.emailChesi, G:chesi@eee.hku.hken_HK
dc.identifier.authorityChesi, G=rp00100en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1109/CDC.2005.1582394en_HK
dc.identifier.scopuseid_2-s2.0-33847205061en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33847205061&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume2005en_HK
dc.identifier.spage1642en_HK
dc.identifier.epage1647en_HK
dc.identifier.scopusauthoridChesi, G=7006328614en_HK
dc.identifier.issnl0743-1546-

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