Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces
We will consider a pole assignment problem for a class of linear neutral functional differential equations in Banach spaces. We will think of the neutral system studied as that of involving no time delays and reduce the study of adjoint semigroups and spectral properties of neutral equations to thos...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/948764 |
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| _version_ | 1850160291906584576 |
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| author | Xuewen Xia Kai Liu |
| author_facet | Xuewen Xia Kai Liu |
| author_sort | Xuewen Xia |
| collection | DOAJ |
| description | We will consider a pole assignment problem for a class of linear neutral functional differential equations in Banach spaces. We will think of the neutral system studied as that of involving no time delays and reduce the study of adjoint semigroups and spectral properties of neutral equations to those of Cauchy problems. Under the
assumption that both the control and eigenspace of pole are finite
dimensional, we establish the rank conditions for finite pole
assignability. |
| format | Article |
| id | doaj-art-b6b5c09e0ef34fdaaa22c93f175fe17c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b6b5c09e0ef34fdaaa22c93f175fe17c2025-08-20T02:23:11ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/948764948764Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach SpacesXuewen Xia0Kai Liu1Faculty of Science, Hunan Institute of Engineering, Xiangtan, Hunan 411104, ChinaDivision of Statistics and Probability, Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, UKWe will consider a pole assignment problem for a class of linear neutral functional differential equations in Banach spaces. We will think of the neutral system studied as that of involving no time delays and reduce the study of adjoint semigroups and spectral properties of neutral equations to those of Cauchy problems. Under the assumption that both the control and eigenspace of pole are finite dimensional, we establish the rank conditions for finite pole assignability.http://dx.doi.org/10.1155/2010/948764 |
| spellingShingle | Xuewen Xia Kai Liu Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces Abstract and Applied Analysis |
| title | Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces |
| title_full | Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces |
| title_fullStr | Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces |
| title_full_unstemmed | Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces |
| title_short | Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces |
| title_sort | spectral properties and finite pole assignment of linear neutral systems in banach spaces |
| url | http://dx.doi.org/10.1155/2010/948764 |
| work_keys_str_mv | AT xuewenxia spectralpropertiesandfinitepoleassignmentoflinearneutralsystemsinbanachspaces AT kailiu spectralpropertiesandfinitepoleassignmentoflinearneutralsystemsinbanachspaces |