Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary ControlReport as inadecuate




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Journal of Function Spaces and ApplicationsVolume 2013 2013, Article ID 274857, 9 pages

Research Article

Department of Mathematics, Bohai University, Jinzhou 121013, China

Beijing 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.

Abstract

We consider a linear distributed parameter bioprocess withboundary control input possessing a time delay. Using a simple boundary feedback law, we showthat the closed-loop system generates a uniformly bounded -semigroup of linear operators undera certain condition with respect to the feedback gain. After analyzing the spectrum configurationof closed-loop system and verifying the spectrum determined growth assumption, we show thatthe closed-loop system is exponentially stable. Thus, we demonstrate that the linear distributedparameter bioprocess preserves the exponential stability for arbitrary time delays.





Author: Fu Zheng, LingLing Fu, and MingYan Teng

Source: https://www.hindawi.com/



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