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

摘要

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 boundedC0-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.