Model reduction with pole-zero placement and high order moment matching

• DOI: 10.1016/j.automatica.2021.110140
• Publication Date: 2022-01-28T22:34:20Z
• Authors: Tudor C. Ionescu; Orest V. Iftime; Ion Necoara
• Keywords: Zero (linguistics); Model order reduction

In this paper, we compute a low order approximation of a system of large order $n$ that matches $��$ moments of order $j_i$ of the transfer function, at $��$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches $��-(\ell +k)$ moments of order $j_i+1$, where $j_i+1$ is the multiplicity of the $i$-th interpolation point. We derive explicit linear systems in the free parameters to simultaneously achieve the required pole-zero placement and match the desired high order moments. We compute the closed form of the free parameters that meet the constraints, as the solution of a $��$ order linear system. Furthermore, for data-driven model reduction, we generalize the construction of the Loewner matrices to include the data and the imposed pole and higher order moment constraints. The resulting approximations achieve a trade-off between the good norm approximation and the preservation of the dynamics of the original system in a region of interest.<br/>7 pages<br/>