On the stability of feedback systems with one diffrentiable nonlinear element

The purpose of this paper is to establish the stability of single-loop feedback systems with one differentiable nonlinear element. In those cases where the Popov criterion fails to guarantee stability for the entire sector predicted by Aizerman´s conjecture, new results can be obtained by restricting the slope of the nonlinear function. A new frequency domain stability criterion is obtained which, like the Popov criterion, has only one unknown parameter. Thus, a simple graphical interpretation is possible. Examples are given which show a considerable improvement over the Popov criterion.