Data-driven Implementations of Various Generalizations of Balanced Truncation

Abstract: There exist two main frameworks for non-intrusive implementations of approximate balanced truncation: the quadrature-based framework and the ADI-based framework. 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 state-space realization. Recently, the quadrature-based framework 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 is theoretically nonintrusive-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.