This paper considers the integrated control of a three highly cooperative vehicles which follow a leader. The leading vehicle can be driven manually and his longitudinal acceleration is not accessible for the followers. Otherwise each vehicle of the string uses front and rear information to achieve speed and reference distance tracking. Thanks to the use of the invariant-set-based theory, the control approach allows that the state trajectories of all the vehicles remain bounded under bounded disturbance inputs, such as leading vehicle acceleration. Handling of variable headway time is made possible through an LPV modelling. Simulation results show an efficient behaviour under various maneuvers.