On Exponential Stability of Parallel-Flow Heat Exchanger Equations with Boundary Feedback

Abstract

This paper is concerned with stability analysis of parallel-flow heat exchanger equations with boundary feedback. The parallel-flow heat exchanger equation is super-stable when the boundary inputs are identically zero. However, when a pole assignment problem is considered, a suitable output feedback law needs to be added to the equation in order to produce finite poles. In this paper, it is shown that a C₀-semigroup generated by the closed-loop operator, which consists of the parallel-flow heat exchanger equation and an output feedback law, satisfies the spectrum determined growth assumption.