Parameterization of All Moment Matching Interpolants

We provide an enhancement of the notion of time-domain moments for systems of nonlinear differential-algebraic equations possessing feedforward terms. Following this, a parameterized family of systems achieving moment matching is given and, under mild conditions, it is shown that this family parameterizes all systems achieving moment matching and having dimension at least as large as that of the signal generator. Finally, we provide a demonstrative example in which a reduced order model achieving moment matching is dynamically extended in order to provide a more accurate approximation of the transient output response of the original system.