On enforcing stability for data-driven reduced-order models

In this paper, we address stability enforcement for reduced-order models computed from data (transfer function measurements). Two data-driven methods based on interpolation will be analyzed: the Loewner framework and the AAA algorithm. They construct reduced-order linear models that may or may not be stable. Hence, it is necessary to apply post-processing methods that yield stable surrogate models. We make use of a projection method that computes the best stable approximation with respect to the infinity norm. Finally, we study the applicability and robustness and of the proposed method through different numerical examples.