Improved model order reduction techniques with error bounds

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.

Keywords:

• Reduced-order model
• frequency-limited-interval
• frequency-weights
• Gramians
• error bound

Acknowledgements

The authors would like to thank the Guangdong Chinese Academy of Science (GDAC) CAS China and National University of Sciences and Technology Pakistan.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

There is no funding involved in this research work.