Dynamic Boundary Stabilization of Linear and Quasi-Linear Hyperbolic Systems

Felipe Castillo Buenaventura 1 Emmanuel Witrant 1 Christophe Prieur 2 Luc Dugard 1
1 GIPSA-SLR - SLR
GIPSA-DA - Département Automatique
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : Systems governed by hyperbolic partial differential equations with dynamics associated with their boundary conditions are considered in this paper. These infinite dimensional systems can be described by linear or quasi-linear hyperbolic equations. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of such systems. A polytopic approach is developed for quasi-linear hyperbolic systems in order to guarantee stability in a given region around an equilibrium point. An isentropic inviscid flow model is used to illustrate some of the main results.
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Felipe Castillo Buenaventura, Emmanuel Witrant, Christophe Prieur, Luc Dugard. Dynamic Boundary Stabilization of Linear and Quasi-Linear Hyperbolic Systems. 51st IEEE Conference on Decision and Control (CDC 2012), Dec 2012, Maui, Hawaï, United States. pp.2952-2957. ⟨hal-00718725⟩

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