This thesis presents theoretical results for stability and string stability of formation control architectures for platooning. We consider three important interconnection topologies for vehicles travelling in a straight line as a string: leader following, cyclic and bidirectional. For the leader following topology we discuss modifications that allow reduced coordination requirements. In the first case we consider the use of the leader velocity as the state to be broadcast to the followers, rather than the standard use of the leader position. This selection yields a formation control architecture that achieves string stability even under time delays in the state broadcast, while reducing typical coordination requirements of leader following architectures. For the second modification we change the way in which the leader position is sent across the string to every follower. This technique keeps some of the good transient properties of the standard leader following architecture but eliminates most of the coordination requirements for the followers. However, we show that this technique does not provide string stability when time delays are present in the communication. The second topology that we discuss is a cyclic one, where the first member of the platoon is forced to track the last one. We discuss two strategies: one where the inter-vehicle spacings may follow a constanttime headway spacing policy and one where an independent leader broadcasts its position to every member of a cyclic platoon. For both strategies we obtain closed form expressions for the transfer functions from disturbances to inter-vehicle spacings. These expressions allow us to show that if the design parameters are not properly chosen, the vehicle platoon may become unstable when the string size is greater than a critical number. On the contrary, if the design parameters are well chosen, both architectures can be made stable and string stable for any size of the platoon. The final topology that we consider is bidirectional, where every member of the platoon, with the exception of the first and last, use measurements of the two nearest neighbours to control their position within the string. Although the derivations are more complex than in the two previous unidirectional cases, we obtain closed form epressions for the dynamics of the platoon. These expressions are in the form of simple transfer functions from disturbances to vehicles. They allow us to obtain stability results for any size of the platoon and understand the behaviour of the least stable pole location as the string size increases. All of the results obtained are illustrated by numerical examples and ad-hoc simulations.