Families of reduced order models that achieve nonlinear moment matching

In this paper we present a time-domain notion of moments for a class of single-input, single-output nonlinear systems, affine in the input, in terms of the steady-state response of the output of a generalized signal generator driven by the nonlinear system. In addition, we define a new notion of moment matching and present the class of (nonlinear) parameterized reduced order models that achieve moment matching. Furthermore, we establish relations with existing notions of moment, showing that the families of reduced order models that achieve nonlinear moment matching are equivalent. Furthermore, we compute the reduced order model that matches moments at two sets of interpolation points, simultaneously, i.e., the number of interpolation points is twice the order of the model.