Cooperative driving has attracted the attention of many research centers around the world as a continuation towards a world with fully autonomous vehicles as full autonomy requires cooperation and coordination among vehicles as well as the ability to move automatically. One of the well-known applications of the cooperative driving is vehicle platooning, where vehicles drive in a single lane with close distance gap for fuel reduction. The formation of platooning is a matter of vehicular communication as well as vehicle control. In this paper, a decentralized novel model-free controller is proposed based on the analysis of longitudinal vehicle and platoon dynamics. The proposed controller has been tested for stability in both analytical and graphical ways and it was tested on a nonlinear model in different simulation platforms; MATLAB/SIMULINK and on CARLA simulator and compared to Sliding Mode Control (SMC) to validate its performance. The results shown that the proposed controller is asymptotically stable and has an accuracy close to SMC but outperforming in computational efficiency.