Mutual transformation of continuous and discrete models of linear dynamic systems

A method for constructing systems of linear difference equations the solutions of which coincide with the solutions of some given linear system of differential equations, is described. An algorithm for solving the inverse problem, that of constructing a system of linear differential equations the solutions of which coincide, at integer-valued time instants, with the solutions of a given system of linear difference equations with real coefficients is also described. It is shown that, in the solution of the inverse problem, the coefficients of the constructed system can turn out to be complex. A method for solving the inverse problem that has the property that the obtained coefficients remain real, but the order of the system is increased, is presented. Examples that illustrate the application of these methods are given.