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

Abstract EN

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.