Further Results on the Structure of Normal Forms of Input-Affine Nonlinear MIMO Systems

In a recent paper it has been shown that the existence, for a MIMO nonlinear system, of normal forms with a special structure that proves to be useful in the design of feedback laws is implied by an assumption introduced a long time ago by Hirschorn in his work on systems invertibility. In this paper, we provide an alternative viewpoint and prove that a necessary and sufficient condition for the existence of such kind of normal forms can be identified in a special feature of the so-called maximal controlled invariant distribution algorithm.