Frequency domain model validation in Wasserstein metric

This paper connects the time-domain uncertainty propagation approach for model validation in Wasserstein distance ₂W₂, introduced by the authors in [1], with the frequency domain model validation in the same. To the best of our knowledge, this is the first frequency domain interpretation of Monge-Kantorovich optimal transport. It is shown that the asymptotic ₂W₂ can be written as functions of the ℌ₂ norms of the system gains, which have intuitive meaning. A geometric interpretation for this newly derived frequency-domain formula is given. The geometric interpretation helps us in comparing Wasserstein distance with classical frequency-domain validation metrics like υ-gap.