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Article: On the gap between positive polynomials and SOS of polynomials

TitleOn the gap between positive polynomials and SOS of polynomials
Authors
Chesi, G
KeywordsHilbert's 17th problem
Linear matrix inequality (LMI)
Optimization
Positive polynomial
Sum of squares (SOS)
Issue Date2007
PublisherIEEE.
Citation
Ieee Transactions On Automatic Control, 2007, v. 52 n. 6, p. 1066-1072 How to Cite?
DOI: http://dx.doi.org/10.1109/TAC.2007.899083
AbstractThis note investigates the gap existing between positive polynomials and sum of squares (SOS) of polynomials, which affects several analysis and synthesis tools in control systems based on polynomial SOS relaxations, and about which almost nothing is known. In particular, a matrix characterization of the PNS, that is the positive homogeneous forms that are not SOS, is proposed, which allows to show that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parametrization of the set of PNS is introduced. © 2007 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/57458
ISSN
0018-9286
2021 Impact Factor: 6.549
2020 SCImago Journal Rankings: 3.436
ISI Accession Number ID
WOS:000247353300010
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.date.accessioned2010-04-12T01:37:16Z-
dc.date.available2010-04-12T01:37:16Z-
dc.date.issued2007en_HK
dc.identifier.citationIeee Transactions On Automatic Control, 2007, v. 52 n. 6, p. 1066-1072en_HK
dc.identifier.issn0018-9286en_HK
dc.identifier.urihttp://hdl.handle.net/10722/57458-
dc.description.abstractThis note investigates the gap existing between positive polynomials and sum of squares (SOS) of polynomials, which affects several analysis and synthesis tools in control systems based on polynomial SOS relaxations, and about which almost nothing is known. In particular, a matrix characterization of the PNS, that is the positive homogeneous forms that are not SOS, is proposed, which allows to show that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parametrization of the set of PNS is introduced. © 2007 IEEE.en_HK
dc.languageengen_HK
dc.publisherIEEE.en_HK
dc.relation.ispartofIEEE Transactions on Automatic Controlen_HK
dc.rights©2007 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.subjectLinear matrix inequality (LMI)en_HK
dc.subjectOptimizationen_HK
dc.subjectPositive polynomialen_HK
dc.subjectSum of squares (SOS)en_HK
dc.titleOn the gap between positive polynomials and SOS of polynomialsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0018-9286&volume=52&issue=6&spage=1066&epage=1072&date=2007&atitle=On+the+gap+between+positive+polynomials+and+SOS+of+polynomialsen_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/TAC.2007.899083en_HK
dc.identifier.scopuseid_2-s2.0-34447125653en_HK
dc.identifier.hkuros130706-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-34447125653&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume52en_HK
dc.identifier.issue6en_HK
dc.identifier.spage1066en_HK
dc.identifier.epage1072en_HK
dc.identifier.isiWOS:000247353300010-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChesi, G=7006328614en_HK
dc.identifier.issnl0018-9286-

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