  This paper presents a control design with integral action for vehicle
platoons with disturbance that ensures string stability of the closed loop and
disturbance rejection. The addition of integral action and a coordinate change
allows to develop sufficient smoothness conditions on the closed loop system to
ensure that the closed loop system using the proposed controller is string
stable in the presence of time-varying disturbances and able able to reject
constant disturbances. In addition, bounds for the tracking error of the
platoon configuration are also given. Further, a case study is considered
together with a suitable controller structure, which satisfies the required
smoothness conditions. Simulation results illustrate the performance of the
closed loop.
