Strictly Proper Control Design for the Stabilization of 2×2 Linear Hyperbolic ODE-PDE-ODE Systems

David Bou Saba (1) , Federico Bribiesca Argomedo (1) , Michaël Di Loreto (1) , Damien Eberard (1)

1 MIS - Ampère, Département Méthodes pour l'Ingénierie des Systèmes

In this paper, we consider the problem of L 2exponential stabilization of a coupled ODE-hyperbolic PDE-ODE system, where actuation is available through one ODE. Based on the backstepping technique, the system is mapped into an equivalent delay form which allows for the construction of a strictly proper controller realized as a full-state feedback. The result extends previous control designs, lifting some restrictions on the structure of the ODEs under consideration and guaranteeing a non-zero delay margin for the closed-loop system.

Domaines: Automatique; Automatique / Robotique; Optimisation et contrôle [math.OC]

David Bou Saba, Federico Bribiesca Argomedo, Michaël Di Loreto, Damien Eberard. Strictly Proper Control Design for the Stabilization of 2×2 Linear Hyperbolic ODE-PDE-ODE Systems. 2019 IEEE 58th Conference on Decision and Control (CDC), Dec 2019, Nice, France. pp.4996-5001, ⟨10.1109/CDC40024.2019.9030248⟩. ⟨hal-03498072⟩