Approximation of singularly perturbed linear hyperbolic systems

Ying Tang (1) , Christophe Prieur (1) , Antoine Girard (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 CASYS - Calculs Algébriques et Systèmes Dynamiques

This paper is concerned with systems modelled by linear singularly perturbed partial differential equations. More precisely a class of linear systems of conservation laws with a small perturbation parameter is investigated. By setting the perturbation parameter to zero, the full system leads to two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics. The exponential stability for both subsystems are obtained by the stability of the overall system of conservation laws. However, the stability of the two subsystems does not imply the stability of the full system. The approximation of the solution for the overall system by the solution for the reduced system is validated via Lyapunov techniques.

Mots clés: Singular perturbation; Approximation; Hyperbolic systems

Domaines: Optimisation et contrôle [math.OC]

Ying Tang, Christophe Prieur, Antoine Girard. Approximation of singularly perturbed linear hyperbolic systems. MTNS 2014 - 21st International Symposium on Mathematical Theory of Networks and Systems, Jul 2014, Groningen, Netherlands. 4 p. ⟨hal-00997291⟩