# 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 (2008)

- 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 (2008): 403-425. <http://eudml.org/doc/90919>.

@article{Tchousso2008,

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 Lp,
$1<p\leq \infty$.
},

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; hyperbolic symmetric systems; strongly continuous semigroups},

language = {eng},

month = {5},

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/90919},

volume = {15},

year = {2008},

}

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

DA - 2008/5//

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 Lp,
$1<p\leq \infty$.

LA - eng

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

UR - http://eudml.org/doc/90919

ER -

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