Identification of a linear model for nonlinear systems

It is shown that the output of a certain class of nonlinear dynamic systems can match arbitrarily close the output of a linear dynamic system if the spectral content of the probing input is the same as that of the output of the nonlinear system. The class of nonlinear systems with cascade or feedback combination of static nonlinear elements and a linear dynamic system is considered. If the static nonlinearity is odd symmetric, and the input signal is periodic, persistently exciting with only odd harmonics then it is shown that an arbitrarily close match between the output of the linear system and the nonlinear system may be achieved. The proposed method differs from the traditional linear approximation model in that it captures the behavior of the nonlinear system over a larger region of the operating point. The proposed scheme is verified on simulated nonlinear systems, and tested on a physical system, and finds application in system identification for control design, fault diagnosis, and analysis of the behavior of the nonlinear system.