Complete identification of a class of nonlinear systems from steady-state frequency response

A solution to the identification problem for a class of nonlinear systems, based on steady-state frequency response, is presented. This class is composed of certain interconnections of stable linear dynamic systems and integer power nonlinearities. Two kinds of measurements are considered. The first involves obtaining the amplitude and relative phase of each harmonic of the steady-state frequency response, while the second involves measuring the amplitudes only. In each case we find the number of measurements sufficient to identify a system for which the highest power present and the bounds on the dimensions of the linear subsystems are known.