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

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 gener...

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Bibliographic Details
Published in:Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-8
Main Authors: Guo, Bao-zhu, Zheng, Fu, Zhang, Yang, Jin, Xue-Lian
Format: Article
Language:English
Subjects:
Cauchy problems
Closed loop systems
Closed loops
Control stability
Control systems
Controllers
Engineering
Feedback control
Heat exchangers
Hilbert space
Physical properties
Semigroups
Stability
System theory
Time lag
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2017/8952647