A novel elementary operation approach with Jordan transformation to order reduction for Roesser state-space model

Abstract

This paper proposes a novel elementary operation approach to order reduction for the Roesser state-space model of multidimensional (n-D) systems by introducing a new kind of transformation, i.e., the Jordan transformation, which guarantees the establishment of an objective matrix with more general structure than the existing one. Then two basic order reduction techniques are developed which can overcome the difficulty encountered by the existing methods and reveal, for the first time, the fact that the order reduction is still possible even when the column (or row) blocks in the related n-D polynomial matrix are full rank. Furthermore, based on the Jordan transformation, an equivalence relationship between two Roesser models after using the elementary operations among the different blocks will be clarified. Although these operations do not directly lower the total order of the model, the partial orders can be changed so that it may nevertheless yield a possibility for further order reduction. It turns out that this new approach includes our previous elementary operation order reduction approach just as a special case. Examples are given to illustrate the details as well as the effectiveness of the proposed approach.