Low-rank balanced truncation of discrete time-delay systems based on Laguerre expansions

• Published in: Journal of the Franklin Institute Vol. 361; no. 6; p. 106752
• Main Authors: Fang, Ya-Xin, Xiao, Zhi-Hua, Qi, Zhen-Zhong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2024
• Subjects: Balanced truncation; Discrete time-delay systems; Laguerre functions; Low-rank Gramians; Model order reduction; Balanced truncation; Low-rank Gramians; Model order reduction; Laguerre functions; Discrete time-delay systems
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2024.106752

This paper introduces a novel model order reduction method based on low-rank Gramian approximations for discrete time-delay systems. Firstly, an efficient algorithm based on Laguerre functions to compute the low-rank decomposition factors of the controllability and observability Gramians for discrete time-delay systems is given, in which the low-rank factors satisfy the iterative recursive formulas of the expansion coefficients of the Laguerre functions. It effectively avoids the direct solutions of Gramians. Then, the reduced-order model of the discrete time-delay system is obtained by combining the low-rank square root method. Additionally, a modified algorithm that combines the dominant subspace projection method is introduced, which alleviates certain drawbacks of the above technique and enhances the stability in certain cases. Finally, two numerical examples are given to verify the accuracy and efficiency of our proposed algorithm. •A low-rank model order reduction algorithm for discrete time-delay systems is presented.•The low-rank factors of the Gramians are calculated iteratively by the Laguerre functions.•An effective strategy is given to produce a stable reduced model under certain conditions.•The efficiency of the proposed algorithm is verified by two given numerical examples.