Contents I. Introduction
A dynamical control system with an output, initialized at some initial state, gives rise to the response map, which assigns to each control (input) defined on the interval the value of the output at time . A realization of an abstract response map consists of a dynamical system with an output, initialized at some initial state, whose response map coincides with the abstract response map. In such a setting, the realization problem was studied by Sontag [1], Jakubczyk [2], and Bartosiewicz [3]. The systems were either polynomial or analytic, with discrete or continuous time. Besides the response map, other input/output representations are widely used. They include the input/output map, the Volterra or Fliess series [4], input/output relations like differential or difference equations of higher order [5]. We refer the reader to overviews [6] and [7], where different approaches are compared and more references can be found.
