Relationships between stability test methods of non-linear control systems†

Abstract

This paper deals with the stability problem of a closed-loop regulator system which contains in its open loop a linear transfer function and a non-linear element. It is concerned with the interrelationship of Popov's theorem, Aizerman's hypothesis, and the describing function. The interrelationship is obtained for a single-valued non-linear element, confined to a finite sector.