# Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method

Abdoua Tchousso; Thibaut Besson; Cheng-Zhong Xu

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 2, page 403-425
- ISSN: 1292-8119

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topTchousso, Abdoua, Besson, Thibaut, and Xu, Cheng-Zhong. "Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2009): 403-425. <http://eudml.org/doc/245513>.

@article{Tchousso2009,

abstract = {In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes and, in particular, exponential stability of heat exchangers. Through concrete examples we show 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 $L^p$, $1<p\le \infty $.},

author = {Tchousso, Abdoua, Besson, Thibaut, Xu, Cheng-Zhong},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {hyperbolic symmetric systems; partial differential equations; exponential stability; strongly continuous semigroups; Lyapunov functionals; heat exchangers},

language = {eng},

number = {2},

pages = {403-425},

publisher = {EDP-Sciences},

title = {Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method},

url = {http://eudml.org/doc/245513},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Tchousso, Abdoua

AU - Besson, Thibaut

AU - Xu, Cheng-Zhong

TI - Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2009

PB - EDP-Sciences

VL - 15

IS - 2

SP - 403

EP - 425

AB - In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes and, in particular, exponential stability of heat exchangers. Through concrete examples we show 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 $L^p$, $1<p\le \infty $.

LA - eng

KW - hyperbolic symmetric systems; partial differential equations; exponential stability; strongly continuous semigroups; Lyapunov functionals; heat exchangers

UR - http://eudml.org/doc/245513

ER -

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