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arXiv · 2509.12393

Data-driven balanced truncation for linear systems with quadratic outputs

Reetish Padhi·Ion Victor Gosea·Igor Pontes Duff·Serkan Gugercin
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Abstract

We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for data-driven balanced truncation of standard linear systems with linear outputs only. The new approach makes use of the time-domain and frequency-domain quadrature-based representation of the system's infinite Gramians, only implicitly. We show that by sampling solely the extended impulse responses of the original system and their derivatives (or the corresponding transfer functions), we construct a reduced-order model that mimics the approximation quality of the intrusive (projection-based) balanced truncation. We validate the proposed framework on a numerical example.

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Reetish Padhi, Ion Victor Gosea, Igor Pontes Duff, Serkan Gugercin. 2025-09-15. Data-driven balanced truncation for linear systems with quadratic outputs. https://doi.org/10.1109/lcsys.2025.3642487

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