A new order reduction approach based on elementary operation for Roesser state-space model

In this paper, a new order reduction approach will be proposed for Roesser state-space model of multidimensional (n-D) systems based on the elementary operation order reduction approach proposed by the co-authors very recently. It will be shown that the n-D order reduction problem can be formulated again into an elementary operation problem of an well-initialized n-D polynomial matrix but the standard objective matrix has a more general form than the existing one. As a consequence, the existing elementary operation order reduction approach can be viewed as a special case of the new proposed approach. Moreover, a basic order reduction procedure is presented and corresponding examples are given to illustrate the details as well as the effectiveness of the proposed approach.