The world is becoming increasingly congested due to a continuous growth of world population and overall wealth. Current road capacity limitations will lead to a significant decrease of traffic flow accompanied by a serious increase in global fuel consumption and air pollution. Ever-expanding road infrastructure is not expected to be a sustainable and long-term solution, thus other solutions are sought. Amongst these solutions is the concept letting AVs drive closer together, cooperatively. A flock of vehicles that coordinates collective movement while maintaining short inter-vehicle distances is defined as platooning. Evidently, in order to achieve safe platooning, a thorough understanding of both longitudinal and lateral behavior of the platoon system and its dynamics is required. The longitudinal aspect of platooning concerned with the design of spacing policies (i.e., distance keeping) has been broadly researched in the past decades. As a consequence, numerous valid applications exist. Whereas for the lateral aspect, the subject has not been researched as extensive. Hence a considerable amount of knowledge on this side is still needed to meet strict conditions and requirements for platooning applications. One of the major bottlenecks obstructing robust lateral platoon control is the ability to assure the lateral string stability for the complete platoon. String stability implies that errors propagating in an upstream direction of inter-connected vehicles forming the vehicular platoon, do not amplify. Specifically, lateral string stability implies that initially bounded lateral errors will remain bounded between ever pair of consecutive vehicles along the string of vehicles. Propagating errors are therefore attenuated during, e.g. the execution of a lane change. Henceforth, when Lateral String Stability for a platoon can be guaranteed, so is the reassurance that a platoon can safely perform certain manoeuvres such as a collective lane change. This thesis endeavours to develop a string stable, lateral controller for a homogeneous platoon of vehicles using a Model Predictive Control (MPC) approach. In the process two different control strategies tightly linked with the information flow topology, being centralized and distributed, are designed and compared in terms of reference tracking performance, noise- and disturbance rejection and practical implementation. Lastly, the developed controllers are simulated and validated using Siemens' Simcenter Prescan software, after which the results are thoroughly discussed. Results have indicated that for the application discussed in this work, the centralized controller outperformed its competitor in the field of tracking performance and noise rejection, but not by a great margin. Furthermore, the novel developed definition of Practical Lateral String Stability (PLSS) guarantees stability for a platoon of n=5 vehicles while using both controllers. To this end, the distributed controller is seen as worthy competitor and more workable solution due to the centralized controller's issue of practical implementation. As part of anticipated future work, we plan testing the proposed approach with field experiments to validate the proposed method in real life.