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Article: Concepts of strict positive realness and the absolute stability problem of continuous-time systems

TitleConcepts of strict positive realness and the absolute stability problem of continuous-time systems
Authors
KeywordsAbsolute Stability
Continuous-Time Systems
Nonlinear Control
Nonlinear Feedback Systems
Wide Strict Positive Realness
Issue Date1998
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automatica
Citation
Automatica, 1998, v. 34 n. 9, p. 1071-1082 How to Cite?
AbstractAfter the conditions for absolute stability and positive realness are reviewed, it is shown that the current definition of positive realness is inadequate to establish less conservative criteria for absolute stability. In this paper, the concepts of wide positive realness (WPR) and wide strict positive realness (WSPR) are proposed. Both WPR and WSPR functions may have poles in the open left and right half-planes, and WPR functions may have single poles on the imaginary axis including ± j ∞. Using the concepts of WPR and WSPR, less conservative criteria, including algebraic and frequency domain criteria, are presented for absolute stability of slope-restricted multiple nonlinearity feedback systems. Refined results for non-slope-restricted non-linearity feedback systems are also proposed. It is pointed out that there is no spectral factorization for WPR and WSPR functions if they have poles at both j ∞ and - j ∞, this can be used to explain the deficiencies of algebraic criteria presented in previous publications. © 1998 Elsevier Science Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/169663
ISSN
2015 Impact Factor: 3.635
2015 SCImago Journal Rankings: 4.315
References

 

DC FieldValueLanguage
dc.contributor.authorXiao, Cen_US
dc.contributor.authorHill, DJen_US
dc.date.accessioned2012-10-25T04:54:04Z-
dc.date.available2012-10-25T04:54:04Z-
dc.date.issued1998en_US
dc.identifier.citationAutomatica, 1998, v. 34 n. 9, p. 1071-1082en_US
dc.identifier.issn0005-1098en_US
dc.identifier.urihttp://hdl.handle.net/10722/169663-
dc.description.abstractAfter the conditions for absolute stability and positive realness are reviewed, it is shown that the current definition of positive realness is inadequate to establish less conservative criteria for absolute stability. In this paper, the concepts of wide positive realness (WPR) and wide strict positive realness (WSPR) are proposed. Both WPR and WSPR functions may have poles in the open left and right half-planes, and WPR functions may have single poles on the imaginary axis including ± j ∞. Using the concepts of WPR and WSPR, less conservative criteria, including algebraic and frequency domain criteria, are presented for absolute stability of slope-restricted multiple nonlinearity feedback systems. Refined results for non-slope-restricted non-linearity feedback systems are also proposed. It is pointed out that there is no spectral factorization for WPR and WSPR functions if they have poles at both j ∞ and - j ∞, this can be used to explain the deficiencies of algebraic criteria presented in previous publications. © 1998 Elsevier Science Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/automaticaen_US
dc.relation.ispartofAutomaticaen_US
dc.subjectAbsolute Stabilityen_US
dc.subjectContinuous-Time Systemsen_US
dc.subjectNonlinear Controlen_US
dc.subjectNonlinear Feedback Systemsen_US
dc.subjectWide Strict Positive Realnessen_US
dc.titleConcepts of strict positive realness and the absolute stability problem of continuous-time systemsen_US
dc.typeArticleen_US
dc.identifier.emailHill, DJ:en_US
dc.identifier.authorityHill, DJ=rp01669en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0032163025en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0032163025&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume34en_US
dc.identifier.issue9en_US
dc.identifier.spage1071en_US
dc.identifier.epage1082en_US
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridXiao, C=7202240414en_US
dc.identifier.scopusauthoridHill, DJ=35398599500en_US

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