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

Abstract

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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 ≤ ∞ .

How to cite

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Tchousso, 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&lt;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&lt;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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