Truncated Order Reduction Methods for Discrete Linear Periodic Time-Varying Systems

In this paper, for the model downgrading problem of single-input single-output (SISO) discrete linear periodic time-varying systems, a truncated order reduction method for the time-varying structure of the period-preserving system is proposed based on the relationship between the state variables and the coefficient matrices. Firstly, the transformation matrix and the reduced-order system are obtained by singular value decomposition (SVD) and truncation of the coefficient matrix, and the corresponding reduced-order algorithm is given. Secondly, some conclusions of the transformation matrix are given, and the output sampling polyphase (OSP) transfer functions of the reduced-order system and the original system are analyzed. In experiments, numerical examples verify the feasibility of the reduced-order method.