Asymptotic stability of a repairable system with imperfect switching mechanism
This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-depend...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.631 |
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| _version_ | 1832558921028468736 |
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| author | Houbao Xu Weihua Guo Jingyuan Yu Guangtian Zhu |
| author_facet | Houbao Xu Weihua Guo Jingyuan Yu Guangtian Zhu |
| author_sort | Houbao Xu |
| collection | DOAJ |
| description | This paper studies the asymptotic stability of a repairable system with
repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and 0 is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue
0. |
| format | Article |
| id | doaj-art-34e024ce6af64daa926bc963c10a44ec |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-34e024ce6af64daa926bc963c10a44ec2025-02-03T01:31:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005463164310.1155/IJMMS.2005.631Asymptotic stability of a repairable system with imperfect switching mechanismHoubao Xu0Weihua Guo1Jingyuan Yu2Guangtian Zhu3Department of Mathematics, Beijing Institute of Technology, 16 Fucheng Road, Beijing 100037, ChinaDepartment of Information and Computing Science, Zhengzhou Institute of Light Industry, Henan 450002, ChinaDepartment of System Engineering, The 710 Institute, 16 Fucheng Road, Beijing 100037, ChinaAcademy of Mathematics and System Science, Chinese Academy of Science, Beijing 100080, ChinaThis paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and 0 is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue 0.http://dx.doi.org/10.1155/IJMMS.2005.631 |
| spellingShingle | Houbao Xu Weihua Guo Jingyuan Yu Guangtian Zhu Asymptotic stability of a repairable system with imperfect switching mechanism International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic stability of a repairable system with imperfect switching mechanism |
| title_full | Asymptotic stability of a repairable system with imperfect switching mechanism |
| title_fullStr | Asymptotic stability of a repairable system with imperfect switching mechanism |
| title_full_unstemmed | Asymptotic stability of a repairable system with imperfect switching mechanism |
| title_short | Asymptotic stability of a repairable system with imperfect switching mechanism |
| title_sort | asymptotic stability of a repairable system with imperfect switching mechanism |
| url | http://dx.doi.org/10.1155/IJMMS.2005.631 |
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