Stability Preserving Model Reduction Technique for Weighted and Limited Interval Discrete-Time Systems With Error Bound

Abstract

The pioneer frequency weighted and limited Gramians based model order reduction techniques presented by Enns and Wang &#x0026; Zilouchian produce unstable reduced-order models for discrete-time systems. To overcome these main drawbacks, many researchers provided a solution to preserve the reduced-order model&#x2019;s stability. However, these existing techniques also produce an unstable reduced-order model in some conditions and produce a large variation to the original system, producing a large approximation error. In this brief, the frequency weighted and limited Gramians based model order reduction technique is presented for the discrete-time systems, which ensure the stability of the reduced-order models and provide low-frequency response approximation error. Furthermore, the proposed technique also provides an easily calculable <i>a priori error bound</i> formula. The proposed work produces steady and precise outcomes compared to conventional reduction methods that show the efficacy of the proposed algorithm.