Estimation of the risk for an unstable behaviour of feedback systems in the presence of nonlinear distortions

A criterion to verify experimentally the stability of a nonlinear system, captured in a feedback loop, is proposed. The basic idea is to split the output power in coherent (linearly related to the input) and noncoherent power (the remaining power). A nonlinear power gain, measuring the sensitivity of the noncoherent output power to input variations, is introduced. Using the small gain theorem, it is possible to check the local stability of the feedback for the actual class of excitation signals: the risk is estimated that the feedback system would become unstable for another realization of the experiment using extreme value statistics.