Enhanced Frequency-Weighted and Frequency Interval Gramians-Based Balanced Truncation

In this paper, we demonstrate a novel solution for the continuous-time frequency-weighted and frequency-interval Gramians-based reduced-order modeling problems using a new structure of input and output matrices. It has been observed that reduced-order models (ROMs) of some methodologies produce unstable ROMs, and the generated ROMs differ substantially from the actual model, resulting in substantial approximation inaccuracy. The proposed frequency-weighted strategy is beneficial as it offers stable ROMs when input and output weightings are utilized. Further, the frequency-interval Gramians-based proposed algorithm also generates stable ROMs. The effectiveness of the presented strategies are shown by numerical examples, and the findings are compared to other well-established frequency-weighted and frequency-interval Gramians-based model order reduction (MOR) methods.