Exponential Stability of a Nonlinear Distributed Parameter System

Abstract

A nonlinear parabolic partial differential equation model describing the behaviour of a distributed parameter fixed-bed bioreactor is studied here. Exponential stability around the steady state solution for exponentially decaying deviations in the input and disturbance are proved via abstract formulation of the model as an evolution equation and by utilizing semigroup theory and asymptotic stability of the corresponding evolution operator.