A global framework for linear stability analyses of traffic models, based on the dispersion relation root locus method, is presented and is applied taking the example of a broad class of car following models. This approach is able to analyse all aspects of the dynamics: long waves and short wave behaviors, phase velocities and stability features. The methodology is applied to investigate the potential benefits of connected vehicles, i.e. V2V communication enabling a vehicle to send and receive information to and from surrounding vehicles. We choose to focus on the design of the coefficients of cooperation which weights the information from downstream vehicles. The coefficients tuning is performed and different ways of implementing an efficient cooperative strategy are discussed. Hence, this paper brings design methods in order to obtain robust stability of traffic models, with application on cooperative car following models.