Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade (Q1086205)

A theorem is presented which validates the use of describing functions to predict the existence and stability of limit cycles arising from feedback systems with an equal number of linear and nonlinear elements which alternate in cascade. The result is based on the theory of integral manifolds and sinusoidal-input describing functions. Furthermore, the quasi-static stability (instability) criteria for the predicted limit cycles are shown to be equivalent to the stability (instability) criteria of the theorem. Two examples are given which illustrate the results of the paper.