Experimental stability analysis of nonlinear feedback systems

It is well known that nonlinear modelling is a very hard task. First, the model selection is problematic. But especially the validation of nonlinear models is time consuming, extremely difficult, and hence expensive; there is no guarantee that the model is good everywhere, and consequently there is a large risk for remaining modelling errors. Due to these modelling errors, even if the model can be shown to be stable, one cannot be perfectly sure that the nonlinear system is stable. As supported by simulation studies, it appears that under certain circumstances (properties of the input signal, e.g. the rms-level), certain nonlinear feedback loops behave stably, while under other circumstances, the same loop behaves occasionally unstably, or even highly unstably, while the analysis of the control loop on the basis of the model guaranteed the stability. This suggests that some input dependent probability of instability should be introduced. The purpose of the method is to give the user guidance, when he suspects potential instability problems due to nonlinearities.