Identification of Low Order Systems in a Loewner Framework

This paper considers the problem of non-parametric identification of low-order models from time-domain experimental data using a combination of Caratheodory Fejer and Loewner-based interpolation, followed by a Loewner matrix Balanced Reduction (LBR) step. As we show in the paper, the Loewner matrix is an estimator for the trace norm of a system, playing a role similar to the one played by the Hankel matrix. However, utilizing Zolotarev numbers to establish decay rate bounds for singular values reveals that the decay of singular values in the Loewner matrix is considerably faster than that in the Hankel matrix. Thus, Loewner-based methods yield lower order systems, with the same error bound, than comparable ones based on Hankel matrices. The effectiveness of our method is demonstrated through a numerical example.