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Model-order reductions for MIMO systems using global Krylov subspace methods

Author

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  • Chu, Chia-Chi
  • Lai, Ming-Hong
  • Feng, Wu-Shiung

Abstract

This paper presents theoretical foundations of global Krylov subspace methods for model order reductions. This method is an extension of the standard Krylov subspace method for multiple-inputs multiple-outputs (MIMO) systems. By employing the congruence transformation with global Krylov subspaces, both one-sided Arnoldi and two-sided Lanczos oblique projection methods are explored for both single expansion point and multiple expansion points. In order to further reduce the computational complexity for multiple expansion points, adaptive-order multiple points moment matching algorithms, or the so-called rational Krylov space method, are also studied. Two algorithms, including the adaptive-order rational global Arnoldi (AORGA) algorithm and the adaptive-order global Lanczos (AOGL) algorithm, are developed in detail. Simulations of practical dynamical systems will be conducted to illustrate the feasibility and the efficiency of proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:4:p:1153-1164
    DOI: 10.1016/j.matcom.2007.09.007
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Rydel, Marek & Stanisławski, Włodzimierz, 2017. "Selection of reduction parameters for complex plant MIMO LTI models using the evolutionary algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 140(C), pages 94-106.

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