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

Abstract

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.

Keywords:

• Model order reduction
• discrete time-delay systems
• discrete Laguerre polynomials
• Taylor expansion

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11871393], China Postdoctoral Science Foundation [grant number 2019M663654], International Science and Technology Cooperation Program of Shaanxi Key Research & Development Plan [grant number 2019KWZ-08] and Shaanxi Natural Science Basic Research Plan [grant number 2020JQ-004].

Notes on contributors

Zhao-Hong Wang

Zhao-Hong Wang is currently pursuing Ph.D at the College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang, China. His research interests are model order reduction for discrete-time systems.

Yao-Lin Jiang

Yao-Lin Jiang is a full professor at the School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, China. He has published four books and about 250 papers in journals. His research interests include theoretical studies of engineering problems, model order reduction, waveform relaxation, numerical solutions of differential equations, dynamics of nonlinear systems, circuit simulation, and parallel processing.

Kang-Li Xu

Kang-Li Xu is currently a post-doctoral fellow at Xi'an Jiaotong University. Her research interests include theoretical studies of nonlinear control systems, model order reduction, and Riemannian optimization.