A new elementary operation approach to multidimensional realization and LFR uncertainty modeling: the SISO case

Abstract

In this paper, a new elementary operation approach is proposed to the problem of multidimensional (n-D) Roesser state-space model realization or linear fractional representation (LFR) uncertainty modeling. The new approach can overcome the main difficulties encountered by Galkowski's approach and always generates a standard or regular realization for a given causal n-D transfer function. In particular, the n-D realization problem is formulated as an elementary operation problem of a certain n-D polynomial matrix in a way totally different from Galkowski's approach so that the singularity problem can be completely avoided. A general constructive realization procedure and an algorithm for evaluating the realization order associated with this procedure will be proposed, which can be easily implemented by symbolic software in, e.g., MATLAB or Maple. Some further techniques for a realization with lower order will also be shown. Symbolic and numerical examples will be presented throughout the paper to illustrate the basic ideas as well as the effectiveness of the proposed approach.