Robustness Issues of the Equivalent Linear Representation of a Nonlinear System

In many engineering applications, linear models are preferred, even if it is known that the system is nonlinear. A large class of nonlinear systems, excited with a ´Gaussian´ random excitation, can be represented as a linear system G_BLA plus a nonlinear noise source Y_S. The nonlinear noise source represents that part of the output that is not captured by the linear approximation. It was shown before that the G_BLA is an invariant for a wide class of excitations with a user specified power spectrum. In this paper it is shown that also the power spectrum S_YS of the nonlinear noise source Y_S is a robust characteristic. This shows that the alternative ´linear representation´ of a nonlinear system is a robust one, making its use in the daily engineering practice very attractive.