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

In this paper, we calculate a low order model of linear system large dimension, that matches set high moments the transfer function and achieves pole-zero placement constraints. The satisfying all constraints simultaneously is selected from family parametrized reduced models. parameters are computed solving an explicit algebraic system. Furthermore, construct Loewner matrices given data imposed first moment resulting approximations achieve trade-off between good norm approximation preservation dynamics in region interest. theory illustrated on academic example cart controlled by double pendulum practical CD player.