Model order reduction of bilinear time-delay systems

In this paper, we present a novel method for approximating bilinear time-delay systems by bilinear systems with no delay. This is performed by means of matching some input-output mappings of the original system in the frequency domain. The method used to construct a bilinear realization is a recent generalization of the so-called Loewner framework. The theoretical claims are supported by numerical results which show that the original system is well approximated both in time and in frequency domain.