On the Stability of a Hysteretic System under Sinusoidal Excitation

ABSTRACT Expressions for the Dual Input Describing Functions (DIDF's) of a two-state relay with hysteresis have been obtained by using an equivalent function generator for the non-linearity. These DIDF's were then applied to analyse the effects of sinusoidal input signals on the stability of a feedback system which includes the hysteretic relay. These results, as substantiated by simulator data, indicate that, besides the stabilizing effects, the presence of sinusoidal signals at the input of the particular system studied may produce dual mode operation over a. range of input amplitudes.