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Article: Stabilization of wave systems with input delay in the boundary control

TitleStabilization of wave systems with input delay in the boundary control
Authors
KeywordsRiesz basis
Stabilization
Time delay
Wave equation
Issue Date2006
PublisherE D P Sciences. The Journal's web site is located at http://www.edpsciences.org
Citation
ESAIM - Control, Optimisation And Calculus Of Variations, 2006, v. 12 n. 4, p. 770-785 How to Cite?
AbstractIn the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 - μ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hubert space. Furthermore, we show that when the weight μ > 1/2, for any time delay, we can choose a suitable feedback gain so that the closed loop system is exponentially stable. When μ = 1/2 we show that the system is at most asymptotically stable. When μ < 1/2, the system is always unstable. © EDP Sciences, SMAI 2006.
Persistent Identifierhttp://hdl.handle.net/10722/75341
ISSN
2015 Impact Factor: 1.112
2015 SCImago Journal Rankings: 1.184
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorXu, GQen_HK
dc.contributor.authorYung, SPen_HK
dc.contributor.authorLi, LKen_HK
dc.date.accessioned2010-09-06T07:10:12Z-
dc.date.available2010-09-06T07:10:12Z-
dc.date.issued2006en_HK
dc.identifier.citationESAIM - Control, Optimisation And Calculus Of Variations, 2006, v. 12 n. 4, p. 770-785en_HK
dc.identifier.issn1292-8119en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75341-
dc.description.abstractIn the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 - μ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hubert space. Furthermore, we show that when the weight μ > 1/2, for any time delay, we can choose a suitable feedback gain so that the closed loop system is exponentially stable. When μ = 1/2 we show that the system is at most asymptotically stable. When μ < 1/2, the system is always unstable. © EDP Sciences, SMAI 2006.en_HK
dc.languageengen_HK
dc.publisherE D P Sciences. The Journal's web site is located at http://www.edpsciences.orgen_HK
dc.relation.ispartofESAIM - Control, Optimisation and Calculus of Variationsen_HK
dc.rightsE S A I M: Control, Optimisation and Calculus of Variations. Copyright © E D P Sciences.en_HK
dc.subjectRiesz basisen_HK
dc.subjectStabilizationen_HK
dc.subjectTime delayen_HK
dc.subjectWave equationen_HK
dc.titleStabilization of wave systems with input delay in the boundary controlen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1292-8119&volume=12&spage=770&epage=785&date=2006&atitle=Stabilization+of+Wave+Systems+with+Input+Delay+in+the+Boundary+Controlen_HK
dc.identifier.emailYung, SP:spyung@hkucc.hku.hken_HK
dc.identifier.authorityYung, SP=rp00838en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1051/cocv:2006021en_HK
dc.identifier.scopuseid_2-s2.0-33749664537en_HK
dc.identifier.hkuros128144en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33749664537&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume12en_HK
dc.identifier.issue4en_HK
dc.identifier.spage770en_HK
dc.identifier.epage785en_HK
dc.identifier.isiWOS:000241191600007-
dc.publisher.placeFranceen_HK
dc.identifier.scopusauthoridXu, GQ=7404263948en_HK
dc.identifier.scopusauthoridYung, SP=7006540951en_HK
dc.identifier.scopusauthoridLi, LK=7501447410en_HK

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