# Symmetric Hermite quadrature-based balanced truncation for learning linear dynamical systems from derivative data

arXiv: https://arxiv.org/abs/2606.00298 · HTML: https://mlsanity.com/paper/2606.00298/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 2 of 2)

- [Data-driven balancing of linear dynamical systems](https://mlsanity.com/paper/2104.01006/) (2021)
- [Data-driven balanced truncation for second-order systems with generalized proportional damping](https://mlsanity.com/paper/2506.10118/) (2025)

## Abstract (arXiv)

Data-driven reduced-order modeling is an essential component in the computer-aided design of control systems. In this work, we present a novel symmetric Hermite formulation of the quadrature-based balanced truncation algorithm that constructs linear reduced-order models from evaluations of the full-order system's transfer function and its derivative. Significantly, the Hermite formulation preserves desirable qualitative properties of the system used to generate the data, such as state-space Hermiticity and, consequently, asymptotic stability.