A New Dual-Input Describing Function and an Application to the Stability of Forced Nonlinear Systems

A new general DIDF (dual input describing function) has been analytically derived for single-valued nonlinearities subjected to two arbitrary noncommensurate sine waves. The development corroborates a previous approximate development for two sine waves widely separated in frequency. The new DIDF is applied to the problem of the stability of nonlinear systems subjected to sinusoidal forcing. It is shown that the conventional DF (describing function) cannot be used for nonautonomous systems without additional safeguards. After it has been shown by the DIDF that no auto-oscillations exist for given input conditions it is proper to employ the conventional DF in any of the methods suggested in the literature to obtain the closed-loop frequency response under those conditions.