Two counterexamples to Aizerman´s conjecture

In the last few years, several sufficient conditions have been found for establishing the asymptotic stability in the large of the null solution of feedback systems containing a single non-linearity. The experiments reported in this paper show that, if these sufficient conditions are violated, in certain cases instability occurs in the form of oscillations. These experiments not only establish a new class of oscillators but they also constitute counterexamples to Aizerman´s conjecture. An explanation of the oscillations is proposed which uses harmonic linearization.