A Study on the Spectrum of the Sampled-Data Transfer Operator with Application to Robust Exponential Stability Problems.
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| Title: | A Study on the Spectrum of the Sampled-Data Transfer Operator with Application to Robust Exponential Stability Problems. |
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| Authors: | Hagiwara, Tomomichi1 hagiwara@kuee.kyoto-u.ac.jp |
| Source: | SIAM Journal on Control & Optimization. 2005, Vol. 44 Issue 1, p313. 15p. |
| Subjects: | Transfer operators, Operator theory, Exponential functions, Eigenvalues, Digital control systems |
| Abstract: | This paper begins by studying some spectral properties of the transfer operators of sampled-data systems described by applying the lifting technique. Through a "nonasymptotic" characterization of the transfer operator, its spectrum is determined in terms of finite-dimensional eigenvalue problems. Then, it is shown that a close connection with such eigenvalue problems and the exponential stability condition can be exploited to study the robust internal (exponential) stability problem of sampled-data systems. Since the transfer operator is relevant to input-output characteristics, the relationship between input-output stability and internal stability is also discussed in the context of sampled-data systems. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 18086096 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Study on the Spectrum of the Sampled-Data Transfer Operator with Application to Robust Exponential Stability Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hagiwara%2C+Tomomichi%22">Hagiwara, Tomomichi</searchLink><relatesTo>1</relatesTo><i> hagiwara@kuee.kyoto-u.ac.jp</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Control+%26+Optimization%22">SIAM Journal on Control & Optimization</searchLink>. 2005, Vol. 44 Issue 1, p313. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Transfer+operators%22">Transfer operators</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+theory%22">Operator theory</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Digital+control+systems%22">Digital control systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper begins by studying some spectral properties of the transfer operators of sampled-data systems described by applying the lifting technique. Through a "nonasymptotic" characterization of the transfer operator, its spectrum is determined in terms of finite-dimensional eigenvalue problems. Then, it is shown that a close connection with such eigenvalue problems and the exponential stability condition can be exploited to study the robust internal (exponential) stability problem of sampled-data systems. Since the transfer operator is relevant to input-output characteristics, the relationship between input-output stability and internal stability is also discussed in the context of sampled-data systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Control & Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/S036301290343682X Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 313 Subjects: – SubjectFull: Transfer operators Type: general – SubjectFull: Operator theory Type: general – SubjectFull: Exponential functions Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Digital control systems Type: general Titles: – TitleFull: A Study on the Spectrum of the Sampled-Data Transfer Operator with Application to Robust Exponential Stability Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hagiwara, Tomomichi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: 2005 Type: published Y: 2005 Identifiers: – Type: issn-print Value: 03630129 Numbering: – Type: volume Value: 44 – Type: issue Value: 1 Titles: – TitleFull: SIAM Journal on Control & Optimization Type: main |
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