This paper is on the design of cooperative adaptive cruise control systems for automated driving of platoons of vehicles in the longitudinal direction. Longitudinal models of vehicles with simple dynamics, an uncertain first order time constant and vehicle to vehicle communication with a communication delay are used in the vehicle modeling. A robust parameter space approach is developed and applied to the design of the cooperative adaptive cruise control system. D-stability is chosen as the robust performance goal and the feedback PD controller is designed in controller parameter space to achieve this D-stability goal for a range of possible longitudinal dynamics time constants and different values of time gap. Preceding vehicle acceleration is sent to the ego vehicle using vehicle to vehicle communication and a feedforward controller is used in this inter-vehicle loop to improve performance. Simulation results of an eight vehicle platoon of heterogeneous vehicles are presented and evaluated to demonstrate the efficiency of the proposed design method. Also, the proposed method is compared with a benchmark controller and the feedback only controller. Time gap regulation and string stability are used to assess performance and the effect of the vehicle to vehicle communication frequency on control system performance is also investigated.