Slow time-varying delay effects - robust stability characterization of deterministic car following models

It is very well known that traffic dynamics are inherently time delayed because of the limited sensing and acting capabilities of drivers against velocity and position sensing. Furthermore, as experimentally validated time delay is not a constant physical entity, but slowly time-varying. However, due to further complications, this has been ignored in the literature up until today, as to our best knowledge. We respond to the question of robust stability with respect to time varying time delays and present sufficient conditions on this time varying component guaranteeing the robust stability of a conceptual traffic flow scenario.