Time domain and frequency domain model order reduction for discrete time-delay systems

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.