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.