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

Xue-Lian Jin, Yang Zhang, Fu Zheng and Bao-zhu Guo

Mathematical Problems in Engineering, 2017, vol. 2017, 1-8

Abstract:

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 -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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8952647

DOI: 10.1155/2017/8952647

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