The Frobenius Theorem

The Frobenius theorem is of exceptional importance both from the point of view of differential geometry and differential topology but also from the Automatic Control and Nonlinear Systems analysis and design point of view. This text aims to be a self-contained report on the Frobenius theorem. First, some necessary definitions are given and basic facts about distributions are stated. The dual objects of distributions - the codistributions are introduced. We try to describe these notions and engage them to involutiveness and complete integrability, to state and prove the Frobenius Theorem which is of great importance in nonlinear control theory.

Ferdinand Georg Frobenius

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