On moment matching of transfer functions and their derivatives

In this paper we study the problem of computing the (family of) reduced order model(s) that satisfy the following properties the systems match the moments of the given to be reduced system and the same property holds for the first order derivatives of the corresponding transfer functions. We prove that such a model exists and compute it. We also study the problem of moment matching for the state-space representations of the first order derivatives of rational transfer functions. Finally, we show that the model that matches the moment of both the given system and its first order derivative is a member of the family of reduced order models whose first order derivatives achieve moment matching.