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Journal of Function Spaces and Applications
Volume 2013, Article ID 274857, 9 pages
Research Article

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

1Department of Mathematics, Bohai University, Jinzhou 121013, China
2Beijing Institute of Information and Control, Beijing 100037, China

Received 9 April 2013; Accepted 20 July 2013

Academic Editor: Gen-Qi Xu

Copyright © 2013 Fu Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.