Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade
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We formulate and prove a theorem which gives a rigorous mathematical justification for the use of describing functions to predict the existence of limit cycles in a multiple nonlinear feedback system and to predict the stability properties of these limit cycles. Our approach uses the classical sinusoidal-input describing function and the theory of integral manifolds. We demonstrate the applicability of our result by means of two specific examples.