Necessary conditions for solving the nonlinear MIMO output regulation problem

Solutions of the output regulation problem in a nonlinear setting invariably target systems presented under some “normal form”. This paper reviews a recently introduced such form for MIMO nonlinear systems and discusses consequent necessary conditions for solving the MIMO nonlinear output regulation problem. As opposed to the (by now classic) form based on the notion of vector relative degree that is only specific to some square invertible MIMO nonlinear systems, the recent form applies to general (not necessarily invertible, nor square) systems. It turns out that, as far as output regulation goes, the recent form fits better some assumptions that have already been used in the context of square invertible systems and, more important, that can still be used (thanks to this particular normal form) in the context of not square ones.