Laguerre-Based Frequency-Limited Balanced Truncation of Discrete-Time Systems

Zhou Song, Qiu-Yan Song () and Umair Zulfiqar
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Zhou Song: School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD 4072, Australia
Qiu-Yan Song: School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China
Umair Zulfiqar: School of Electronic Information and Electrical Engineering, Yangtze University, Jingzhou 434023, China

Mathematics, 2025, vol. 13, issue 3, 1-15

Abstract: This paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid the computationally expensive generalized Lyapunov equation solvers used in traditional methods. These algorithms employ recursive formulas to calculate Laguerre expansion coefficients, which are then used to derive low-rank decomposition factors for frequency-limited controllability and observability Gramians. Additionally, we enhance the Laguerre-based low-rank MOR algorithm by incorporating a modified frequency-limited BT method, further improving its computational efficiency. Numerical simulations validate the effectiveness of the proposed approach, demonstrating significant reductions in computational complexity while maintaining accuracy in system approximation.

Keywords: model order reduction; frequency-limited; balanced truncation; Laguerre functions; discrete-time systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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