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Eigenvalue trim approach to exact order reduction for roesser state-space model of multidimensional systems

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Abstract

In this paper, a new notion of eigenvalue trim or co-trim for n-D Roesser (state-space) model is first introduced, which reveals the internal connection between the eigenvalues of the system matrix and the reducibility of the considered Roesser model. Then, new reducibility conditions and the corresponding order reduction algorithms based on eigenvalue trim or co-trim are proposed for exact order reduction of a given n-D Roesser model, and it will be shown that this eigenvalue trim approach can be applied even to those systems for which the existing approaches cannot do any further order reduction. Furthermore, a new transformation for n-D Roesser models, by swapping certain rows and columns and interchanging certain entries that belong to different blocks corresponding to different variables, will be established, which can transform an n-D Roesser model whose order cannot be reduced any more by the proposed approach to another equivalent Roesser model with the same order so that this transformed Roesser model can still be reduced further. Examples are given to illustrate the details as well as the effectiveness of the proposed approach.

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Authors and Affiliations

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

    Dongdong Zhao & Li Xu

  2. School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, China

    Shi Yan

Authors
  1. Dongdong Zhao
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  2. Shi Yan
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  3. Li Xu
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Corresponding author

Correspondence to Li Xu.

Additional information

This work was partly supported by the Japan Society for the Promotion of Science (JSPS.KAKENHI15K06072), the National Natural Science Foundation of China (No. 61104122) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-136).

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Zhao, D., Yan, S. & Xu, L. Eigenvalue trim approach to exact order reduction for roesser state-space model of multidimensional systems. Multidim Syst Sign Process 29, 1905–1934 (2018). https://doi.org/10.1007/s11045-017-0536-2

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  • DOI: https://doi.org/10.1007/s11045-017-0536-2

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