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Exponential Stability and Transfer Functionsof Processes Governed by Symmetric Hyperbolic Systems

Published online by Cambridge University Press:  15 September 2002

Cheng-Zhong Xu and
Gauthier Sallet
Cheng-Zhong Xu
Affiliation:
Inria (CORIDA, CONGE) & ESA 7035 du CNRS (MMAS), bâtiment A, Université de Metz, 57045 Metz Cedex 01, France; xu@loria.fr.
Gauthier Sallet
Affiliation:
Inria (CORIDA, CONGE) & ESA 7035 du CNRS (MMAS), bâtiment A, Université de Metz, 57045 Metz Cedex 01, France; sallet@loria.fr.
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Abstract

In this paper we study the frequency andtime domain behaviour of a heat exchanger network system.The system is governed by hyperbolic partial differentialequations. Both the control operator and the observation operator are unbounded but admissible. Using the theoryof symmetric hyperbolic systems, we prove exponentialstability of the underlying semigroup for the heat exchangernetwork. Applying the recent theory of well-posedinfinite-dimensional linear systems, we prove that thesystem is regular and derive various properties of itstransfer functions, which are potentially useful forcontroller design. Our results remain valid for a wide classof processes governed by symmetric hyperbolic systems.

Keywords

Heat exchangerssymmetric hyperbolic equationsexponential stabilityregular systemstransfer functions.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002, pp. 421 - 442
Copyright
© EDP Sciences, SMAI, 2002

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