The Frobenius theorem of differential geometry provides necessary and sufficient conditions for a distribution to be completely integrable. This has important implications on the design of controllers and observers for nonlinear systems. In this presentation we go through all necessary definitions in order to state the Frobenius theorem. These are the notions of a Lie bracket, distribution, involutive and completely integrable distribution, codistribution and annihilator of a distribution. We then state the Frobenius theorem and explain its logical depth.
