Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control
We consider a linear distributed parameter bioprocess with boundary control input possessing a time delay. Using a simple boundary feedback law, we show that the closed-loop system generates a uniformly bounded -semigroup of linear operators under a certain condition with respect to the feedback gai...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/274857 |
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| _version_ | 1850216392167522304 |
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| author | Fu Zheng LingLing Fu MingYan Teng |
| author_facet | Fu Zheng LingLing Fu MingYan Teng |
| author_sort | Fu Zheng |
| collection | DOAJ |
| description | We consider a linear distributed parameter bioprocess with
boundary control input possessing a time delay. Using a simple boundary feedback law, we show
that the closed-loop system generates a uniformly bounded -semigroup of linear operators under
a certain condition with respect to the feedback gain. After analyzing the spectrum configuration
of closed-loop system and verifying the spectrum determined growth assumption, we show that
the closed-loop system is exponentially stable. Thus, we demonstrate that the linear distributed
parameter bioprocess preserves the exponential stability for arbitrary time delays. |
| format | Article |
| id | doaj-art-3bf9b01e7b8441cdb629b461d4ecc4e2 |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-3bf9b01e7b8441cdb629b461d4ecc4e22025-08-20T02:08:19ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/274857274857Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary ControlFu Zheng0LingLing Fu1MingYan Teng2Department of Mathematics, Bohai University, Jinzhou 121013, ChinaDepartment of Mathematics, Bohai University, Jinzhou 121013, ChinaBeijing Institute of Information and Control, Beijing 100037, ChinaWe consider a linear distributed parameter bioprocess with boundary control input possessing a time delay. Using a simple boundary feedback law, we show that the closed-loop system generates a uniformly bounded -semigroup of linear operators under a certain condition with respect to the feedback gain. After analyzing the spectrum configuration of closed-loop system and verifying the spectrum determined growth assumption, we show that the closed-loop system is exponentially stable. Thus, we demonstrate that the linear distributed parameter bioprocess preserves the exponential stability for arbitrary time delays.http://dx.doi.org/10.1155/2013/274857 |
| spellingShingle | Fu Zheng LingLing Fu MingYan Teng Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control Journal of Function Spaces and Applications |
| title | Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control |
| title_full | Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control |
| title_fullStr | Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control |
| title_full_unstemmed | Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control |
| title_short | Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control |
| title_sort | exponential stability of a linear distributed parameter bioprocess with input delay in boundary control |
| url | http://dx.doi.org/10.1155/2013/274857 |
| work_keys_str_mv | AT fuzheng exponentialstabilityofalineardistributedparameterbioprocesswithinputdelayinboundarycontrol AT linglingfu exponentialstabilityofalineardistributedparameterbioprocesswithinputdelayinboundarycontrol AT mingyanteng exponentialstabilityofalineardistributedparameterbioprocesswithinputdelayinboundarycontrol |