Essential orders and the non-linear decoupling problem

The concept of essential orders has recently been introduced into linear system theory and has been shown to be useful in the solution of static and dynamic decoupling problems (Commauit et al. 1986, De Luca et al. 1985). This paper presents a non-trivial extension to the class of non-linear affine systems of some of these definitions and results. It is shown that these invariant integers give the minimal order for a regular dynamic compensator that decouples a right-invertible system.