Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control

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: Fu Zheng, LingLing Fu, MingYan Teng
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2013/274857
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spelling doaj-3bf9b01e7b8441cdb629b461d4ecc4e22020-11-24T22:01:20ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Fu Zheng
LingLing Fu
MingYan Teng
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
author_facet Fu Zheng
LingLing Fu
MingYan Teng
author_sort Fu Zheng
title 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_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_sort exponential stability of a linear distributed parameter bioprocess with input delay in boundary control
publisher Hindawi Limited
series Journal of Function Spaces and Applications
issn 0972-6802
1758-4965
publishDate 2013-01-01
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.
url http://dx.doi.org/10.1155/2013/274857
work_keys_str_mv AT fuzheng exponentialstabilityofalineardistributedparameterbioprocesswithinputdelayinboundarycontrol
AT linglingfu exponentialstabilityofalineardistributedparameterbioprocesswithinputdelayinboundarycontrol
AT mingyanteng exponentialstabilityofalineardistributedparameterbioprocesswithinputdelayinboundarycontrol
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