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