The only stable normal forms of affine systems under feedback are linear

We consider the problem of existence of structurally stable normal forms of affine control systems with m inputs and n-dimensional state space, equipped with C^∞-Whitney topology and acted on by the static state feedback group. It is proved that structurally stable normal forms exist only if m = n or m =1 and n = 2, and are linear. There are no stable normal forms in any other range of dimensions (m, n).