Exponential Stability of a Linear Distributed Parameter Bioprocess with Input Delay in Boundary Control. (6th August 2013)

• Record Type: Journal Article
• Authors: Zheng, Fu; Fu, LingLing; Teng, MingYan
• Other Names: Xu Gen-Qi Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-08-06
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/274857
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : 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 C 0 -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.