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Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials

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  • Li, Yanpeng
  • Jiang, Yaolin
  • Yang, Ping

Abstract

This paper investigates time domain model order reduction of discrete-time bilinear systems with inhomogeneous initial conditions. The state of the system is approximated by the power series associated with the Charlier polynomials and the recurrence relation of the expansion coefficients is derived. The expansion coefficients are orthogonalized to construct the projection matrix by the modified multi-order Arnoldi method. The output of the resulting reduced order system maintains a certain number of expansion coefficients of the original output, and the error estimation of the reduced order system is briefly discussed. Due to the fact that the projection matrix involves the information of initial conditions, the proposed method can well reduce discrete-time bilinear systems with inhomogeneous initial conditions. Two numerical examples are employed to illustrate the effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:905-920
    DOI: 10.1016/j.matcom.2021.06.021
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    References listed on IDEAS

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    1. Pulch, Roland, 2019. "Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 76-92.
    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.
    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. Kawaji, S. & Shiotsuki, T., 1985. "Model reduction by walsh function techniques," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 27(5), pages 479-484.
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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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