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Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions

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

Abstract

This paper investigates model order reduction (MOR) methods of discrete-time systems via discrete orthogonal polynomials in the time domain. First, this system is expanded under discrete orthogonal polynomials, and the expansion coefficients are computed from a linear equation. Then the reduced-order system is produced by using the orthogonal projection matrix that is defined in terms of the expansion coefficients, which can match the first several expansion coefficients of the original output, and preserve the asymptotic stability and bounded-input/bounded-output (BIBO) stability. We also study the output error between the original system and its reduced-order system. Besides, the MOR method using discrete Walsh functions is proposed for discrete-time systems with inhomogeneous initial conditions. Finally, three numerical examples are given to illustrate the feasibility of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:53:y:2022:i:10:p:2045-2062
    DOI: 10.1080/00207721.2022.2037780
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    Cited by:

    1. 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.

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