Model order reduction based on discrete-time Laguerre functions for discrete linear periodic time-varying systems

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.