We detail in this article the development of a delay-robust stabilizing feedback control law for a linear ordinary differential equation coupled with two linear first order hyperbolic equations in the actuation path. The proposed method combines the use of a backstepping approach, required to construct a cancelling feedback for the in-domain coupling terms of the PDEs, with a second change of variables that reduces the stabilization problem of the PDE-ODE system to that of a time-delay system for which a predictor can be constructed. The proposed controller can be tuned, with some restrictions imposed by the system structure, either by adjusting a reflection coefficient left on the PDE after the backstepping transformation, or by choosing the pole placement on the ODE when constructing the predictor, enabling a trade-off between convergence rate and delay-robustness. The proposed feedback law is finally proved to be robust to small delays in the actuation

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.