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On minimal realizations of first-degree 3D systems with separable denominators

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Abstract

In this paper, we focus on first-degree three-dimensional (3D) causal systems which have separable denominators. Gröbner basis is applied to prove that not all first-degree 3D systems with separable denominators have minimal realizations (of order 3). This is in contrast to 2D systems with separable denominators which always admit absolutely minimal realizations. Two illustrative examples are presented.

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Acknowledgments

We wish to acknowledge the funding support for this project from Nanyang Technological University under the Undergraduate Research Experience on Campus (URECA) program.

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Authors and Affiliations

  1. School of Physics and Mathematics Sciences, Nanyang Technological University, Singapore, Singapore

    Thi Loan Nguyen

  2. Department of Electronics and Information Systems, Akita Prefectural University, Akita, 015-0055, Japan

    Li Xu

  3. School of EEE, Nanyang Technological University, Singapore, Singapore

    Zhiping Lin

  4. Department of Engineering, LaTrobe University, Bundoora, Australia

    David B. H. Tay

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  1. Thi Loan Nguyen
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  2. Li Xu
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  3. Zhiping Lin
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  4. David B. H. Tay
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Correspondence to Li Xu.

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Nguyen, T.L., Xu, L., Lin, Z. et al. On minimal realizations of first-degree 3D systems with separable denominators. Multidim Syst Sign Process 28, 305–314 (2017). https://doi.org/10.1007/s11045-016-0405-4

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  • DOI: https://doi.org/10.1007/s11045-016-0405-4

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