2025/06/29 by Zulfiqar, Umair, Song, Qiu-Yan, Xiao, Zhi-Hua +1
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2506.23204
There exist two main approaches for non-intrusive implementations of approximate balanced truncation within the Loewner framework: the quadrature-based method [1] and the Alternating Direction Implicit (ADI)-based method [2]. Both approaches rely solely on samples of the transfer function to construct truncated balanced models, eliminating the need for access to the original model's statespace realization. Recently, the quadrature-based approach has been extended to various generalizations of balanced truncation, including positive-real balanced truncation, bounded-real balanced truncation, and balanced stochastic truncation. While this extension [3] is theoretically non-intrusive-meaning it does not require the original state-space realization-it depends on samples of spectral factorizations of the transfer function. Since practical methods for obtaining such samples are currently unavailable, this extension remains largely a theoretical contribution. In this work, we present a non-intrusive ADI-type framework for these generalized balanced truncation methods that requires only samples of the original transfer function for implementation.