Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems

Cheng-Zhong Xu; Gauthier Sallet

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • Volume: 7, page 421-442
  • ISSN: 1292-8119

Abstract

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In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is regular and derive various properties of its transfer functions, which are potentially useful for controller design. Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems.

How to cite

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Xu, Cheng-Zhong, and Sallet, Gauthier. "Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems." ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 421-442. <http://eudml.org/doc/245161>.

@article{Xu2002,
abstract = {In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is regular and derive various properties of its transfer functions, which are potentially useful for controller design. Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems.},
author = {Xu, Cheng-Zhong, Sallet, Gauthier},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {heat exchangers; symmetric hyperbolic equations; exponential stability; regular systems; transfer functions; well-posedness},
language = {eng},
pages = {421-442},
publisher = {EDP-Sciences},
title = {Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems},
url = {http://eudml.org/doc/245161},
volume = {7},
year = {2002},
}

TY - JOUR
AU - Xu, Cheng-Zhong
AU - Sallet, Gauthier
TI - Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2002
PB - EDP-Sciences
VL - 7
SP - 421
EP - 442
AB - In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is regular and derive various properties of its transfer functions, which are potentially useful for controller design. Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems.
LA - eng
KW - heat exchangers; symmetric hyperbolic equations; exponential stability; regular systems; transfer functions; well-posedness
UR - http://eudml.org/doc/245161
ER -

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Citations in EuDML Documents

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  1. Iasson Karafyllis, Miroslav Krstic, On the relation of delay equations to first-order hyperbolic partial differential equations
  2. Abdoua Tchousso, Thibaut Besson, Cheng-Zhong Xu, Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method
  3. Abdoua Tchousso, Thibaut Besson, Cheng-Zhong Xu, Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method
  4. Krzysztof Bartecki, A general transfer function representation for a class of hyperbolic distributed parameter systems

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