Spurious predictions of limit cycles in a non-linear feedback system by the describing function method

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Abstract
It is known that the describing function method can fail to predict limit cycles which do in fact exist. We wish to draw attention to a different mode of failure, where the method predicts limit cycles which do not exist. A surprising feature of the example we give is that the linear part of the system has excellent low-pass properties, unlike the linear parts used in examples of the other failure mode.

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