Upper bounding the variations of the best linear approximation of a nonlinear system in a power sweep measurement

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 random excitations, can be represented as Y = G_BLAU + Y_S, with G_BLA the best linear approximation, and Y_S a nonlinear noise source that represents that part of the output that is not captured by the linear approximation. Because G_BLA not only depends upon the linear dynamics, but also on the nonlinear distortions, it will vary if the input power is changed. In this paper, we study under what conditions (class of excitations, class of nonlinear systems) these variations of G_BLA can be bounded, starting from the knowledge of the power spectrum S_YS. Since S_YS can be easily measured using well designed measurement procedures, it becomes possible to provide the designer with an upper bound for the variations of G_BLA, leading to more robust design procedures.