Describing functions revisited

The well-known graphical describing function procedure can be simply modified to provide a completely reliable method for predicting whether or not certain kinds of nonlinear feedback system can oscillate. The modified method is easy to use and quantifies, in a natural way, the usual intuitive ideas about describing function reliability. In addition to the usual graphs, the user has to draw a band which measures the amount of uncertainty introduced by the approximations inherent in the method; in return for this extra work, the method gives error bounds for oscillation predictions, as well as ranges of frequency and amplitude over which oscillation is impossible. The main restriction is that the nonlinear element must be single valued and have bounded slope.