Qualitative analysis of oscillations in nonlinear control systems: A describing function approach

We present a rigorous analysis of the stability of oscillations in a wide class of nonlinear control systems with numerator dynamics. The analysis employs the classical sinusoidual-input describing function, elementary control theory, and the theory of integral manifolds. We demonstrate, by means of specific examples, how the present results can be used to obtain detailed information concerning the behavior of solutions.