Title: A Symmetric Hermite Quadrature Approach to Balanced Truncation for Learning Linear Dynamical Systems from Derivative Data

Abstract: Developing data-driven reduced-order models is a critical step in the computer-aided design of control systems. This study introduces a new symmetric Hermite formulation for the quadrature-based balanced truncation algorithm, which generates linear reduced-order models using evaluations of both the transfer function and its derivatives from the full-order system. Notably, this Hermite approach maintains key qualitative attributes of the source system, including state-space Hermiticity, which in turn ensures asymptotic stability.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC