INTERPOLATION-BASED MODEL ORDER REDUCTION FOR POLYNOMIAL SYSTEMS

In this work, we investigate a model-order reduction scheme for polynomial systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order system, interpolating the defined generalized transfer functions at a given set of interpolation points. Furthermore, we provide a method, inspired by the Loewner approach for linear and (quadratic-)bilinear systems, to determine a good-quality reduced-order system in an automatic way. We also discuss the computational issues related to the proposed method and a potential application of a CUR matrix approximation in order to further speed up simulation of the reduced-order systems. We test the efficiency of the proposed method via two benchmark examples.