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Exponential stability of distributed parameter systemsgoverned by symmetric hyperbolic partial differential equations usingLyapunov's second method

Published online by Cambridge University Press:  30 May 2008

Abdoua Tchousso ,
Thibaut Besson  and
Cheng-Zhong Xu
Abdoua Tchousso
Affiliation:
LAGEP, Bâtiment CPE, Université Claude Bernard, Lyon I, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France. Departement de Mathématiques et Informatique, Université Abdou Moumouni de Niamey, BP 10662, Niger; xu@lagep.univ-lyon1.fr
Thibaut Besson
Affiliation:
LAGEP, Bâtiment CPE, Université Claude Bernard, Lyon I, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France.
Cheng-Zhong Xu
Affiliation:
LAGEP, Bâtiment CPE, Université Claude Bernard, Lyon I, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France.
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Abstract

In this paper we study asymptotic behaviour of distributed parameter systems governedby partial differential equations (abbreviated to PDE). We first review some recently developed resultson the stability analysis of PDE systems by Lyapunov's second method. On constructing Lyapunov functionalswe prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDEsystems. Then we apply the result to establish exponential stability of various chemical engineeringprocesses and, in particular, exponential stability of heat exchangers. Through concrete examples weshow how Lyapunov's second method may be extended to stability analysis of nonlinear hyperbolic PDE.Meanwhile we explain how the method is adapted to the framework of Banach spaces Lp , $1<p\leq \infty$ . 


Keywords

Hyperbolic symmetric systemspartial differential equationsexponential stabilitystrongly continuous semigroupsLyapunov functionalsheat exchangers

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 2 , April 2009 , pp. 403 - 425
Copyright
© EDP Sciences, SMAI, 2008

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