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

• DOI: 10.3390/math13030448
• Publication Date: 2025-01-29T08:26:10Z
• Authors: Zhou Song; Qiu-Yan Song; Umair Zulfiqar
• Keywords: model order reduction; balanced truncation; discrete-time systems; QA1-939; frequency-limited; Laguerre functions; Mathematics

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.