New Results On Partial Fraction Based Frequency Weighted Balanced Truncation Technique For Discrete–Time System

Abstract

Artikel in membentangkan keputusan baru bagi kaedah pengurangan model frekuensi tertimbang berdasarkan kaedah pengembangan fraksi separa didalam masa diskrit. Rangka pengurangan model bagi kaedah baru yang dicadangkan diperolehi melalui pemotongan langsung, menghasilkan kesalahan yang lebih rendah berbanding kaedah–kaedah lain yang sudah ada. Kaedah baru ini dijamin akan stabil bahkan untuk tertimbang bersisi ganda. Sebuah batas kesalahan a priori yang mudah dan senang dihitung juga diperoleh. Contoh berangka dengan perbandingan dengan teknik yang ada menunjukkan keberkesanan kaedah yang dicadangkan Kata kunci: Rangka pengurangan model; batas kesalahan; kaedah pengembangan fraksi spara In this paper, we present some new results on frequency weighted model reduction technique based on partial fraction expansion idea in discrete–time system. The reduced order models of the newly proposed method obtained by direct truncation, produces lower errors when compared to existing techniques. The new method is guaranteed to be stable even for double sided weightings. A simple and easily computable a priori error bound is also derived. Numerical examples with comparisons to the existing techniques show the effectiveness of the proposed method. Key words: Model order reductions; error bounds; partial fraction expansion