Stability of oscillations in low-order nonlinear systems

Loeb´s criterion and the incremental-input describing function (IDF) stability technique are compared for general nonlinear second- and third-order systems. Situations in which the two stability techniques disagree are determined and studied in detail. The IDF stability technique is related directly to the variational approach for a general system, and Loeb´s criterion is related to that for second-order systems. The IDF stability technique is shown to involve the approximation of time averaging in addition to the inherent describing function (DF) approximation. Discrepancies between the two are found to coincide with relatively poor DF approximations. One technique cannot be considered better than the other in applications-they should be used together for proper interpretation.