Improved model order reduction techniques with error bounds

Shabana Bashrat, Muhammad Imran, Safia Akram, Abdul Wakeel, Nauman Anwar Baig and Asim Zaheer Ud-Din

International Journal of Systems Science, 2024, vol. 55, issue 4, 687-700

Abstract: This paper introduces two enhanced model order reduction techniques designed for scenarios involving frequency-weighted and frequency-limited-interval Gramians in the continuous-time domain. The primary objective is to address the instability issue identified in existing approaches in the continuous-time domain, as formulated by Enns for frequency-weighted scenarios and Gawronski & Juang for frequency-limited-interval scenarios. Despite numerous solutions proposed in the literature to mitigate this problem, a persistent challenge remains the high approximation error between the original and reduced-order systems. To overcome this limitation, the proposed improved techniques focus on ensuring stability in reduced-order models while simultaneously minimising the approximation error between the original and reduced systems. Furthermore, these enhanced techniques provide a computationally straightforward, a priori error bound formula. Numerical findings underscore the correctness and efficiency of the proposed techniques in reducing the approximation error while maintaining stability, thereby substantiating their efficacy.

Date: 2024
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DOI: 10.1080/00207721.2023.2293683

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