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...
| Published in: | Journal of Function Spaces and Applications |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Online Access: | http://dx.doi.org/10.1155/2013/274857 |
| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |