Minimal realization of nonlinear MIMO equations in state-space form: Polynomial approach

The realization of nonlinear input-output equations in the classical state-space form can be studied by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. The aim of the present paper is to apply the polynomial methods to the realization problem. This allows to simplify the step-by-step algorithm based on certain sequences of subspaces of differential one-forms. The presented new formula allows to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. This method is more clear, straight-forward and therefore better suited for implementation in different computer packages such as Mathematica or Maple. The developed theory and algorithm are illustrated by means of several examples.