<p>This paper presents a novel parametric model order reduction (MOR) method specifically developed for discrete-time parameter-varying systems. The main contribution lies in extending non-parametric reduction techniques, previously established for continuous-time systems, to the discrete-time framework. By employing a bilinearization strategy, the parameter-varying system is transformed into an equivalent discrete-time bilinear form through the introduction of auxiliary input functions derived from the Taylor expansion of the parameter-dependent matrices. To efficiently approximate the Gramians of the resulting bilinear system, a Laguerre function-based low-rank approximation is proposed, enabling accurate and computationally efficient evaluation of the system’s dominant dynamics. The reduced-order model is then constructed using projection matrices obtained via singular value decomposition. The proposed approach effectively addresses non-affine parameter dependencies, providing a more precise and scalable reduction framework for large-scale systems. Numerical examples demonstrate the accuracy and computational efficiency of the proposed method in approximating complex discrete-time parameter-varying systems.</p>

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Model order reduction of discrete-time parameter-varying systems via bilinearization and low-rank Gramian approximation

  • Xiao-Rui Tang,
  • Zhi-Hua Xiao,
  • Yao-Lin Jiang

摘要

This paper presents a novel parametric model order reduction (MOR) method specifically developed for discrete-time parameter-varying systems. The main contribution lies in extending non-parametric reduction techniques, previously established for continuous-time systems, to the discrete-time framework. By employing a bilinearization strategy, the parameter-varying system is transformed into an equivalent discrete-time bilinear form through the introduction of auxiliary input functions derived from the Taylor expansion of the parameter-dependent matrices. To efficiently approximate the Gramians of the resulting bilinear system, a Laguerre function-based low-rank approximation is proposed, enabling accurate and computationally efficient evaluation of the system’s dominant dynamics. The reduced-order model is then constructed using projection matrices obtained via singular value decomposition. The proposed approach effectively addresses non-affine parameter dependencies, providing a more precise and scalable reduction framework for large-scale systems. Numerical examples demonstrate the accuracy and computational efficiency of the proposed method in approximating complex discrete-time parameter-varying systems.