Towards a solution of the state-space realization problem of a set of multi-input multi-output nonlinear difference equations

The paper deals with nonlinear system described by the set of higher-order difference equations in the inputs and the outputs. A theorem for transforming such a system around a regular equilibrium point into a locally equivalent one, but having the so-called row- and column-reduced form, is formulated. The importance of this form comes from the fact that this is a suitable starting point for studing the realization problem for a set of nonlinear multi-input multi-output difference equations.