Abstract
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).
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