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

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  • Xue-Lian Jin
  • Yang Zhang
  • Fu Zheng
  • Bao-zhu Guo

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.

Suggested Citation

  • Xue-Lian Jin & Yang Zhang & Fu Zheng & Bao-zhu Guo, 2017. "Exponential Stability of the Monotubular Heat Exchanger Equation with Time Delay in Boundary Observation," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, June.
    • Handle: RePEc:hin:jnlmpe:8952647
    DOI: 10.1155/2017/8952647
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