Describing Function

The describing function (DF) method of Nikolay Mitrofanovich Krylov and Nikolay Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by an LTI system transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior.

Read more about Describing FunctionThe Method, Caveats

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Describing Function - Caveats
... Although the describing function method can produce reasonably accurate results for a wide class of systems, it can fail badly for others ... are fulfilled, there are no periodic solutions by describing function method, but counterexamples with periodic solutions (hidden oscillation) are well known ... Therefore, the application of the describing function method requires additional justification ...

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