  A novel delay-based spacing policy for the control of vehicle platoons is
introduced together with a notion of disturbance string stability. The
delay-based spacing policy specifies the desired inter-vehicular distance
between vehicles and guarantees that all vehicles track the same spatially
varying reference velocity profile, as is for example required for heavy-duty
vehicles driving over hilly terrain. Disturbance string stability is a notion
of string stability of vehicle platoons subject to external disturbances on all
vehicles that guarantees that perturbations do not grow unbounded as they
propagate through the platoon. Specifically, a control design approach in the
spatial domain is presented that achieves tracking of the desired spacing
policy and guarantees disturbance string stability with respect to a spatially
varying reference velocity. The results are illustrated by means of
simulations.
