A moment matching approach for systems of delayed differential equations

In this paper we propose a moment matching approach for approximating time-delay systems with delays in the states. This approach is based on the unique solution of an associated Sylvester-like equation. It results in a family of parametrized, finite-dimensional, reduced order models that match a set of prescribed moments of the given delay-system. We show that, by properly choosing the free parameters, we obtain a finite-dimensional approximation that achieves moment matching at both the zero and first order derivatives of the transfer function of the given delay-system. This approach does not require the explicit computation of the transfer function and its derivatives. We illustrate the potential of this method with a simple example of a state delay-system. The constructed reduced order model for this delay-system is more accurate than approximations obtained using the well-known Padé approximation.