Measuring the stability of nonlinear feedback systems

This paper is concerned with measuring the stability or instability of nonlinear feedback systems. For such kinds of systems, it may happen that the stable or unstable behaviour depends on the nature of the (stochastic) input signal. E.g. the system can show a stable behaviour at low amplitudes, and an unstable behaviour at high amplitudes. In between there can be a transition zone between low and high probabilities of instability. Although the measurement of instability phenomena is relevant for the instrumentation and measurement society, it has not been handled inside this community. This paper partly fills this gap, by introducing a stability definition, and proposing a method that makes a statistical statement about the stable or unstable operation condition of the nonlinear feedback system, starting from input-output measurements.