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In this contribution, we propose a detailed study of interpolation-baseddata-driven methods that are of relevance in the model reduction and also inthe systems and control communities. The data are given by samples of thetransfer function of the underlying (unknown) model, i.e., we analyzefrequency-response data. We also propose novel approaches that combine some ofthe main attributes of the established methods, for addressing particularissues. This includes placing poles and hence, enforcing stability ofreduced-order models, robustness to noisy or perturbed data, and switching fromdifferent rational function representations. We mention here the classicalstate-space format and also various barycentric representations of the fittedrational interpolants. We show that the newly-developed approaches yield, insome cases, superior numerical results, when comparing to the establishedmethods. The numerical results include a thorough analysis of various aspectsrelated to approximation errors, choice of interpolation points, or placingdominant poles, which are tested on some benchmark models and data-sets.

Practical challenges in data-driven interpolation: dealing with noise, enforcing stability, and computing realizations