  In formation control, an ensemble of autonomous agents is required to
stabilize at a given configuration in the plane, doing so while agents are
allowed to observe only a subset of the ensemble. As such, formation control
provides a rich class of problems for decentralized control methods and
techniques. Additionally, it can be used to model a wide variety of scenarios
where decentralization is a main characteristic. We introduce here some
mathematical background necessary to address questions of stability in
decentralized control in general and formation control in particular. This
background includes an extension of the notion of global stability to systems
evolving on manifolds and a notion of robustness of feedback control for
nonlinear systems. We then formally introduce the class of formation control
problems, and summarize known results.
