Many engineering problems can be modelled as linear periodic time-varying (LPTV) systems, which naturally leads to the need for model order reduction of LPTV systems. This paper investigates a new model order reduction method for discrete LPTV systems. First, the state-space realization in the Fourier-lifted form of discrete LPTV system is constructed by representing periodic matrices in exponentially modulated periodic (EMP) Fourier series. By using Laguerre functions to expand the transfer function of the resulting Fourier-lifted system, the corresponding model order reduction algorithm is developed. Furthermore, the proposed algorithm is used to reduce the discrete LPTV system in the standard-lifted form. Theoretical analysis indicates that the transfer functions of both reduced order systems can match a certain number of moments. Finally, two numerical examples are given to verify the effectiveness of the proposed method.

中文翻译：

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基于离散时间拉盖尔函数的离散线性周期时变系统模型降阶

许多工程问题可以建模为线性周期时变 (LPTV) 系统，这自然导致需要对 LPTV 系统进行模型降阶。本文研究了一种新的离散 LPTV 系统模型降阶方法。首先，离散 LPTV 系统傅里叶提升形式的状态空间实现是通过表示指数调制周期 (EMP) 傅里叶级数中的周期矩阵来构建的。通过使用拉盖尔函数扩展得到的傅立叶提升系统的传递函数，开发了相应的模型降阶算法。此外，所提出的算法用于以标准提升形式减少离散LPTV系统。理论分析表明，两种降阶系统的传递函数都可以匹配一定数量的矩。最后，