Novel Frequency‐Weighted Truncated Balanced Realization for 2‐D Decoupled Denominator‐Type Discrete‐Time Systems

ABSTRACT

Effective frequency‐weighted model order reduction (FWMR) for two‐dimensional (2‐D) discrete‐time systems is essential for high‐speed digital filtering and complex signal processing. However, existing FWMR techniques are fundamentally limited either by the severe computational burden of iterative algorithms and complex Lyapunov inequalities, or by the unacceptably large errors caused by the uneven eigenvalue distribution in current methods. Therefore, this article presents a novel FWMR technique designed for 2‐D decoupled denominator‐type discrete‐time systems to solve these crucial bottlenecks. The core innovation lies in a direct block‐diagonalization strategy applied to the weighted Gramian matrices. Furthermore, the methodology algebraically guarantees the stability of the reduced‐order models under both single‐ and double‐sided frequency weightings. The effectiveness of the proposed approach is comprehensively validated through the performance analysis of three distinct computational 2‐D examples, demonstrating significant improvements over existing state‐of‐the‐art frameworks.