Exponential Stability of the Monotubular Heat Exchanger Equation with Time Delay in Boundary Observation

الملخص EN

The exponential stability of the monotubular heat exchanger equation with boundary observation possessing a time delay and inner control was investigated.

Firstly, the close-loop system was translated into an abstract Cauchy problem in the suitable state space.

A uniformly bounded C0-semigroup generated by the close-loop system, which implies that the unique solution of the system exists, was shown.

Secondly, the spectrum configuration of the closed-loop system was analyzed and the eventual differentiability and the eventual compactness of the semigroup were shown by the resolvent estimates on some resolvent sets.

This implies that the spectrum-determined growth assumption holds.

Finally, a sufficient condition, which is related to the physical parameters in the system and is independent of the time delay, of the exponential stability of the closed-loop system was given.