An heterogeneous vehicle platoon controller for autonomous vehicles is proposed in this paper. The traction force of each vehicle is controlled according to the state of the predecessor vehicle, which can be known by LiDAR/RADAR, and the state of the leader vehicle, which is received by vehicle-to-vehicle (V2V) communication. Platoon string stability is evaluated under Lyapunov and H8 conditions. An iterative procedure is proposed in order to deal with the non-convexity of the static output feedback control design problem. Simulation results demonstrate that the proposed heterogeneous vehicle platoon controller achieves a good overall performance without compromising the safety of any vehicle. The separation between each follower and its predecessor is kept in appropriate ranges, always close to the desired reference. Furthermore, the transient errors are not amplificated when propagated downstream the platoon, therefore string stability is assured. Keywords: Autonomous vehicles, heterogeneous vehicle platoon, vehicle platoon control, string stability, output feedback control, robust control, Linear Matrix Inequality