Diffusion and robustness of boundary feedback stabilization of hyperbolic systems

We consider the problem of boundary feedback control single-input-single-output one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue output stabilization is that it requires dynamic laws include delayed values (directly or through state observers) which may not be robust to infinitesimal uncertainties on characteristic velocities. purpose this paper highlight some features by addressing an unstable open-loop system made up two interconnected transport equations provided with anti-located actuation. contribution show robustness against delay recovered as soon arbitrary small diffusion present in system. Our analysis also reveals effect stability far from being obvious exhibiting alternative simple example where presence has a destabilizing instead.