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 c0-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. © 2013 fu zheng et al.