Elementary operation approach to Fornasini–Marchesini state-space model realization of multidimensional systems

Shi, Yan; Zhao, Dongdong; Wang, Hai; Xu, Li

doi:10.1016/j.jfranklin.2020.05.049

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Remark It is worth pointing out that the new defined mapping function

{\mathcal {R}}

can be viewed as a more general case studied in refs. [9, 18]. In contrast to the mapping function of those papers the new defined mapping function

{\mathcal {R}}

involves a submatrix P 22 , which makes it possible to consider the matrix D during the establishment of an SNDRM (see more details in Theorem 3).…”

Section: Admissible Transformation and Degree Reductionmentioning

confidence: 99%

“…Thus, completely different from regular cases, calculating an appropriate D will be one of the essential problems in the SNDRM realization. Moreover, for the considered case, the realization orders obtained for its right and left matrix fractional descriptions (MFDs) are in general different, and thus in practice, the realization with a lower order should be chosen [16,18]. However, different to the regular Roesser model, for the general SNDRM, the duality between a transfer matrix and its transpose does not hold.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Huo

et al. 2023

IET Control Theory & Appl

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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.

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“…Remark It is worth pointing out that the new defined mapping function