Lyapunov stability of a singularly perturbed system of two conservation laws

Ying Tang 1 Christophe Prieur 1 Antoine Girard 2
1 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : This paper is concerned with a class of singularly perturbed systems of two conservation laws. A small perturbation parameter is introduced in the dynamics and the boundary conditions. By setting the perturbation parameter to zero, the singularly perturbed system of conservation laws can be treated as two subsystems of one conservation law: the reduced system and the boundary-layer system. The asymptotic stability of the complete system is investigated via Lyapunov techniques. A Lyapunov function for the singularly perturbed system is obtained as a weighted sum of two Lyapunov functions of the subsystems.
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Ying Tang, Christophe Prieur, Antoine Girard. Lyapunov stability of a singularly perturbed system of two conservation laws. CPDE 2013 - 1st IFAC Workshop on Control of Systems Modeled by Partial Differential Equations, Sep 2013, Paris, France. pp.227-232, ⟨10.3182/20130925-3-FR-4043.00050⟩. ⟨hal-00839621⟩

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