An iterative realization-free approach for model reduction of bilinear systems via Hermitian interpolation

Abstract

In this work, we investigate the approximation and model reduction of bilinear dynamical systems having a particular dynamical structure, such as time-delayed terms, second-order, or fractional derivatives. By means of Volterra series expansion, such systems can be characterized using generalized multivariate transfer functions. Our main goal is to construct unstructured reduced-order bilinear models as reduced models by using evaluations of the generalized multivariate transfer functions associated with the original system. To this aim, we propose a new setup for the bilinear Loewner framework that enables Hermitian interpolation conditions. Moreover, inspired by the TF-IRKA method, we propose an iterative procedure that constructs accurate bilinear reduced models. A numerical test case illustrates the practical applicability of the method.