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Article: On the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam
Title | On the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam |
---|---|
Authors | |
Keywords | C0-Semigroup Differentiable Semigroup Riesz Basis Stability |
Issue Date | 2005 |
Publisher | Elsevier 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? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/156126 |
ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 1.503 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Guo, BZ | en_US |
dc.contributor.author | Wang, JM | en_US |
dc.contributor.author | Yung, SP | en_US |
dc.date.accessioned | 2012-08-08T08:40:30Z | - |
dc.date.available | 2012-08-08T08:40:30Z | - |
dc.date.issued | 2005 | en_US |
dc.identifier.citation | Systems And Control Letters, 2005, v. 54 n. 6, p. 557-574 | en_US |
dc.identifier.issn | 0167-6911 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156126 | - |
dc.description.abstract | In 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.language | eng | en_US |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/sysconle | en_US |
dc.relation.ispartof | Systems and Control Letters | en_US |
dc.subject | C0-Semigroup | en_US |
dc.subject | Differentiable Semigroup | en_US |
dc.subject | Riesz Basis | en_US |
dc.subject | Stability | en_US |
dc.title | On the C0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yung, SP:spyung@hkucc.hku.hk | en_US |
dc.identifier.authority | Yung, SP=rp00838 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/j.sysconle.2004.10.006 | en_US |
dc.identifier.scopus | eid_2-s2.0-17844405303 | en_US |
dc.identifier.hkuros | 109438 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-17844405303&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 54 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.spage | 557 | en_US |
dc.identifier.epage | 574 | en_US |
dc.identifier.isi | WOS:000229108400005 | - |
dc.publisher.place | Netherlands | en_US |
dc.identifier.scopusauthorid | Guo, BZ=7403276431 | en_US |
dc.identifier.scopusauthorid | Wang, JM=7701333092 | en_US |
dc.identifier.scopusauthorid | Yung, SP=7006540951 | en_US |
dc.identifier.issnl | 0167-6911 | - |