Describing function analysis of nonlinear systems with parametric uncertainties

Periodic phenomena, such as limit cycles, are among the most prominent features of nonlinear control systems. Predictions as to whether or not oscillations of this kind are likely to exist can be made using the describing function approach. Here, some of the now well established robustness results regarding linear systems are combined with the describing function method to analyze the stability of autonomous uncertain systems with separable nonlinearities. An example is provided to substantiate the mathematical derivations and theoretical conclusions.