The only stable normal forms of affine systems under feedback are linear
It is shown for which ranges of dimensions (m,n) smooth affine control systems \(\dot x=f(x)+\sum^{m}_{i=1}u_ ig_ i(x)\), \(x\in {\mathbb{R}}^ n\), possess structurally stable normal forms with respect to the static feedback group. Such stable forms exist only if \(m=n\) or if \(m=1\) and \(n=2\) and are, in these cases, linear.
scientific article; zbMATH DE number 4045586
scientific article