Existence and uniqueness of minimal realizations for a class of C∞ systems

The main result is relative to the quotient of a manifold M by a closed discrete equivalence relation when the First homotopy group of M has no infinite order element. As a direct consequence of the main theorem, the existence and uniqueness of minimal realizations is proved for a class of C∞ completely controllable weakly observable systems. This extends : - some results of SUSSMANN availabie in the analytic or symetric cases. - some results of the authors obtained in the compact case.