This paper explores model order reduction (MOR) methods for discrete time-delay systems in the time domain and the frequency domain. First, the discrete time-delay system is expanded under discrete Laguerre polynomials, and the discrete Laguerre coefficients of the system are obtained by a matrix equation. After that, the reduced order system is obtained by using the projection matrix based on these coefficients. Theoretical analysis shows that the resulting reduced order system can preserve a certain number of discrete Laguerre coefficients of output variables in the time domain. We also derive the error bound in the time domain. Furthermore, in order to obtain the moments of the system, we approximate the transfer function of the discrete time-delay system by Taylor expansion. The basis matrices of the higher order Krylov subspace are deduced by a iterative process. Further, we prove that the reduced order system can match a desired number of moments of the original system. The error estimation is obtained in the frequency domain. Finally, two illustrative examples are given to verify the effectiveness of the proposed methods.

中文翻译：

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离散时滞系统的时域和频域模型降阶

本文探讨了时域和频域中离散时滞系统的模型降阶 (MOR) 方法。首先将离散时滞系统在离散拉盖尔多项式下展开，通过矩阵方程得到系统的离散拉盖尔系数。之后，使用基于这些系数的投影矩阵得到降阶系统。理论分析表明，所得到的降阶系统可以在时域中保留一定数量的输出变量的离散拉盖尔系数。我们还推导出时域中的误差界限。此外，为了获得系统的矩，我们通过泰勒展开来近似离散时滞系统的传递函数。高阶 Krylov 子空间的基矩阵是通过迭代过程推导出来的。此外，我们证明了降阶系统可以匹配原始系统所需的矩数。在频域中获得误差估计。最后，给出了两个说明性例子来验证所提出方法的有效性。