This paper starts by deriving a factorization of the Loewner matrix pencil that appears in the data-driven modeling approach known as the Loewner framework and explores its consequences. The first is that the associated quadruple constructed from the data yields a model without requiring further processing. The second consequence is related to how sensitive the eigenvalues of the Loewner pencil are to perturbations. Based on an explicit generalized eigenvalue decomposition of this pencil and by making use of perturbation theory of matrix pencils, we explore two types of eigenvalue sensitivities. The first one is defined with respect to unstructured perturbations of the Loewner pencil, while the second one is defined for structured perturbations. We also discuss how the choice of data affects the two sensitivities.

翻译：本文首先从Lewner矩阵铅笔的乘数出发,它出现在称为Lewner框架的数据驱动模型方法中,并探讨其后果。首先,从数据中得出的相关四重体积产生一个模型,无需进一步处理。第二个后果涉及Lewner铅笔的叶值对扰动的敏感度。根据这一铅笔的明显的电子值分解法,通过使用矩阵铅笔的扰动理论,我们探讨了两种类型的电子价值敏感度。第一个是针对Lewner铅笔的无结构扰动而定义的,第二个是针对结构扰动而定义的。我们还讨论了数据选择如何影响两种敏感度。