  We detail in this article the necessity of a change of paradigm for the
delay-robust control of systems composed of two linear first order hyperbolic
equations. One must go back to the classical trade-off between convergence rate
and delay-robustness. More precisely, we prove that, for systems with strong
reflections, canceling the reflection at the actuated boundary will yield zero
delay-robustness. Indeed, for such systems, using a backstepping-controller,
the corresponding target system should preserve a small amount of this
reflection to ensure robustness to a small delay in the loop. This implies, in
some cases, giving up finite time convergence.
