# Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

Cheng-Zhong Xu; Gauthier Sallet

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topXu, 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 (2010): 421-442. <http://eudml.org/doc/90629>.

@article{Xu2010,

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.; heat exchangers; regular systems; transfer functions; well-posedness},

language = {eng},

month = {3},

pages = {421-442},

publisher = {EDP Sciences},

title = {Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems},

url = {http://eudml.org/doc/90629},

volume = {7},

year = {2010},

}

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

DA - 2010/3//

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.; heat exchangers; regular systems; transfer functions; well-posedness

UR - http://eudml.org/doc/90629

ER -

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