Non-commutative determinants in nonlinear control theory: Preliminary ideas

The paper suggests how to compute the order of the minimal realization of the discrete-time nonlinear control system, described by the set of input-output difference equations, or alternatively, by the two polynomial matrices with the entries in the non-commutative skew polynomial ring. For that purpose the Ore determinant is specified further by including certain additional restrictions and proved that under these additional restrictions the degree of the dieudonne determinant is equal to the degree of the Ore determinant. Finally, the system order is shown to be equal to the degree of the determinant of one polynomial matrix. Only the special case of two output systems is considered in this paper.