This dissertation solves variations of three mathematical problems for autonomous vehicle formations: (1) formation shape control in the plane, (2) robust information architecture design, and (3) formation attitude synchronization. An autonomous vehicle formation is a collection of vehicles, each with computation, communication, sensing, and control capabilities, that cooperate to achieve a common objective. Accelerating advancements are making possible a range of science and engineering applications, such as satellite formations for deep-space imaging, teams of unmanned aircraft for military reconnaissance and surveillance missions, and submarine swarms for oceanic exploration. The ubiquitous potential of these applications is driving theoretical work on autonomous vehicle formations across a range of disciplines. A major theoretical question in the field of control theory, and the main focus of this dissertation, is how the properties of the information architecture (i.e. a mapping of the information flow amongst the agents), relate to the stability properties of the desired shape and orientation under certain control laws. A secondary focus is how to design the information flow so that loss of an agent does not destroy the formation's ability to maintain a desired shape. As a motivating example, a solution to a coordinated standoff tracking problem is presented to demonstrate how an instance of a class of information architectures, which are called persistent and related to rigid graph theory, can be used to achieve a formation objective in a practical scenario involving a team of unmanned aircraft. A generalized formation shape control problem is then solved for a class of persistent architectures. This solution gives only local stability results; global stability is analyzed for a four-agent formation and several open problems are identified. The problem of agent loss is addressed by performing a self-repair operation in the event of agent loss and separately by designing robustness into the information architecture a priori. Finally, a rigid body attitude synchronization problem with communication time delays is solved for a class of information architectures based on spectral graph theory.