Dynamic Boundary Stabilization of First Order Hyperbolic Systems

Felipe Castillo (1) , Emmanuel Witrant (1) , Christophe Prieur (2) , Luc Dugard (1)

1 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

In this chapter, we address the problem of the dynamic boundary stabilization of linear, quasilinear and LPV first-order hyperbolic systems. We provide sufficient conditions for the exponential stability for this class of infinite dimensional systems by means of Lyapunov based techniques and matrix inequalities. We develop an applicative example of a temperature boundary control in a Poiseuille flow using some of our main results and we present simulation results that illustrate the efficiency of our approach.

Mots clés: hyperbolic systems; dynamic boundary stabilization; Lyapunov

Domaines: Automatique / Robotique

Felipe Castillo, Emmanuel Witrant, Christophe Prieur, Luc Dugard. Dynamic Boundary Stabilization of First Order Hyperbolic Systems. Witrant E., Fridman E., Sename O., Dugard L. Recent results on time-delay systems: analysis and control, 5, Springer, pp.169-190, 2016, Serie : Advances in Delays and Dynamics 978-3-319-26367-0. ⟨10.1007/978-3-319-26369-4_9⟩. ⟨hal-01272739⟩