Time-domain moment matching for multiple-input multiple-output linear time-invariant models

Model reduction by moment matching for linear time-invariant (LTI) models is a reduction technique that has a clear interpretation in the Laplace domain. In particular, for the multiple-input multiple-output (MIMO) LTI case, Krylov subspace methods aim at matching the transfer-function matrix (and possibly its derivatives) of the reduced-order model to the transfer-function matrix of the full-order model along so-called tangential directions at desired interpolation points. A straightforward application of time-domain moment matching to MIMO LTI models does not result in such a match in the transfer-function matrix. In this paper, we derive a relation between the MIMO transfer-function matrices of the full- and the reduced-order models that follows from the application of time-domain moment matching on MIMO LTI models. This is subsequently exploited to formulate conditions on the parameters of time-domain moment matching under which the transfer-function matrix is matched along tangential directions, thus ensuring consistency with classical Krylov subspace methods.