Symmetric Hermite Quadrature‐Based Balanced Truncation for Learning Linear Dynamical Systems From Derivative Data

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.