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Article: On the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam

TitleOn the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam
Authors
KeywordsC0-Semigroup
Differentiable Semigroup
Riesz Basis
Stability
Issue Date2005
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/sysconle
Citation
Systems And Control Letters, 2005, v. 54 n. 6, p. 557-574 How to Cite?
AbstractIn this paper, we show that a linear unbounded operator associated with an Euler-Bernoulli beam equation under shear boundary feedback generates a C0-semigroup in the underlying state Hilbert space. This provides an answer to a long time unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green's function and the verification of the Riesz basis property for the generalized eigenfunctions. As a consequence, we show that this semigroup is differentiable and exponentially stable, which is in sharp contrast to the properties possessed by most feedback controlled beams based on a passive design principle. © 2005 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156126
ISSN
2015 Impact Factor: 1.908
2015 SCImago Journal Rankings: 2.323
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorGuo, BZen_US
dc.contributor.authorWang, JMen_US
dc.contributor.authorYung, SPen_US
dc.date.accessioned2012-08-08T08:40:30Z-
dc.date.available2012-08-08T08:40:30Z-
dc.date.issued2005en_US
dc.identifier.citationSystems And Control Letters, 2005, v. 54 n. 6, p. 557-574en_US
dc.identifier.issn0167-6911en_US
dc.identifier.urihttp://hdl.handle.net/10722/156126-
dc.description.abstractIn this paper, we show that a linear unbounded operator associated with an Euler-Bernoulli beam equation under shear boundary feedback generates a C0-semigroup in the underlying state Hilbert space. This provides an answer to a long time unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green's function and the verification of the Riesz basis property for the generalized eigenfunctions. As a consequence, we show that this semigroup is differentiable and exponentially stable, which is in sharp contrast to the properties possessed by most feedback controlled beams based on a passive design principle. © 2005 Elsevier B.V. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/sysconleen_US
dc.relation.ispartofSystems and Control Lettersen_US
dc.subjectC0-Semigroupen_US
dc.subjectDifferentiable Semigroupen_US
dc.subjectRiesz Basisen_US
dc.subjectStabilityen_US
dc.titleOn the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beamen_US
dc.typeArticleen_US
dc.identifier.emailYung, SP:spyung@hkucc.hku.hken_US
dc.identifier.authorityYung, SP=rp00838en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.sysconle.2004.10.006en_US
dc.identifier.scopuseid_2-s2.0-17844405303en_US
dc.identifier.hkuros109438-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-17844405303&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume54en_US
dc.identifier.issue6en_US
dc.identifier.spage557en_US
dc.identifier.epage574en_US
dc.identifier.isiWOS:000229108400005-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridGuo, BZ=7403276431en_US
dc.identifier.scopusauthoridWang, JM=7701333092en_US
dc.identifier.scopusauthoridYung, SP=7006540951en_US

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