Bounds on modeling error due to weak nonlinear distortions

Small nonlinearities affect the measurement of the frequency response function (FRF). The measured best linear approximation to the (nonlinear) system becomes offset from G₀(jω) (the underlying linear system) and the measurements appear noisy due to the presence of the stochastic nonlinear component. Using repeated measurements the characteristics can be smoothed; the bias however presents a problem. In this contribution the authors show, that for a particular class of nonlinear systems, the unknown bias can be bounded even if no a priori information is available about the order or the magnitude of the nonlinear component