Flatness of nonlinear control systems and exterior differential systems

Necessary and sufficient conditions for k-flatness are given. We construct an exterior differential system (I, Θ) and show that (local) k-flatness is equivalent to the existence of (local) integral manifolds of (I, Θ), which is in turn equivalent to the existence of a solution of a partial differential equation. As a consequence, the k-flatness of a nonlinear system can be checked with convenient applications of Cartan-Kahler and Cartan-Kuranishi theorems. Some academic examples are presented to illustrate the result.

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