Data-Driven Model Reduction by Two-Sided Moment Matching

In this brief paper, we propose a time-domain data-driven method for model order reduction by two-sided moment matching for linear systems. An algorithm that asymptotically approximates the matrix product $\mathrm{{\rm Y}}\mathrm{\Pi }$ from time-domain samples of the so-called two-sided interconnection is provided. Exploiting this estimated matrix, we determine the unique reduced-order model of order $\nu$, which asymptotically matches the moments at $2\nu$ distinct interpolation points. Furthermore, we discuss the impact that certain disturbances and data distortions may have on the algorithm. Finally, we illustrate the use of the proposed methodology by means of a benchmark model.