Admissible transformation approach to Roesser state‐space model realization of singular multidimensional systems

Abstract

The problem of the singular Roesser (state-space) model realization of non-causal multivariate transfer (function) matrices is investigated. Specifically, the notion of so-called admissible transformation is introduced, which allows to introduce and investigate a novel invariant matrix relationship on polynomial matrices. The singular multidimensional Roesser model (SNDRM) realization is transformed to the problem of how to reduce an initial polynomial matrix associated with the given transfer matrix into the objective polynomial matrix with a specific structure. Construction procedures are developed to obtain SNDRMs by applying admissible transformations on the initial polynomial matrix. Moreover, a separated standard form is introduced for an SNDRM so that the proposed approach can effectively treat both the left and right matrix fractional descriptions of a noncausal multivariate transfer matrix in a unified manner. Non-trivial examples are provided to illustrate the details and effectiveness of the proposed approach.