Incipient divergence detection in feedback control loops: A controller falsifier

The paper tackles the controller falsification problem in the framework of switching supervisory control. The study is based on applying a suitable form of the small gain stability lemma. This enables one to select a disturbance insensitive statistic in the form of a ratio of closed-loop variables whose level either stays below some threshold if the feedback loop is stable (with false alarm probability as close to zero as we wish), or goes well above the threshold as soon as the feedback variables tend to diverge (with instability detection probability close to one as we wish).