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Reduced-order state-space models for two-dimensional discrete systems via bivariate discrete orthogonal polynomials

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  • Wang, Zhao-Hong
  • Jiang, Yao-Lin
  • Xu, Kang-Li

Abstract

This paper investigates the new model order reduction (MOR) methods via bivariate discrete orthogonal polynomials for two-dimensional (2-D) discrete systems. The 2-D discrete system is described by the Kurek model. First, we deduce algebraically the shift-transformation matrix of the classical discrete orthogonal polynomials of one variable. By means of the shift-transformation matrices, 2-D discrete systems are expanded in the spaces spanned by bivariate discrete orthogonal polynomials. The coefficient matrices are calculated from matrix equations. Then the reduced-order systems are produced by the orthogonal projection matrices defined by the coefficient matrices. Theoretical analysis shows that the reduced-order systems can match a certain number of coefficient vectors of the original outputs. Finally, one numerical example is simulated to demonstrate the feasibility and effectiveness of the proposed methods.

Suggested Citation

  • Wang, Zhao-Hong & Jiang, Yao-Lin & Xu, Kang-Li, 2023. "Reduced-order state-space models for two-dimensional discrete systems via bivariate discrete orthogonal polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 441-456.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:441-456
    DOI: 10.1016/j.matcom.2023.05.009
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    References listed on IDEAS

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    1. Bonin, Thomas & Faßbender, Heike & Soppa, Andreas & Zaeh, Michael, 2016. "A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 1-19.
    2. Zhao-Hong Wang & Yao-Lin Jiang & Kang-Li Xu, 2022. "Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(10), pages 2045-2062, July.
    3. Chu, Chia-Chi & Lai, Ming-Hong & Feng, Wu-Shiung, 2008. "Model-order reductions for MIMO systems using global Krylov subspace methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1153-1164.
    4. Li, Yanpeng & Jiang, Yaolin & Yang, Ping, 2021. "Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 905-920.
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    2. Bonin, Thomas & Faßbender, Heike & Soppa, Andreas & Zaeh, Michael, 2016. "A fully adaptive rational global Arnoldi method for the model-order reduction of second-order MIMO systems with proportional damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 1-19.
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