About a normal “column-form” for nonlinear discrete-time perturbed control systems

It is known that discrete-time singularly perturbed (DSP) dynamics do not exhibit a unique canonical representation. A study in the linear context is developed in Naidu and Rao (1958), Naidu (1988) and Mahmoud (1982) with respect to discrete-time and sampled dynamics showing that at least three different normal forms can be assumed for representing a linear discrete time singularly perturbed system (linear DSPS). Starting from the generalization of these concepts to a nonlinear context, the present work studies the properties for the existence of a nonlinear column-form representation of a nonlinear DSPS