Abstract
A necessary and sufficient frequency domain criterion is developed for investigating the asymptotic stability of oscillations in feedback systems with frequency-dependent non-linearities. The new criterion, which utilizes the describing function theory, assumes two exponentially damped (or divergent) sideband sine wave components for the perturbation term, and invokes the Routh-Hurwitz test. It is shown that this stability criterion can replace more accurately the synchronous incremental-input describing function technique derived for dynamic-type non-linearities. Two examples are solved to demonstrate the applicability of the method presented.
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