Describing function

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The Describing function method of Krylov and Bogolyubov is an approximate procedure for analyzing Non-linear control problems. It is based on quasi-linearization, that is the replacement of the non-linear system under investigation by a system that is linear except for a dependence on the amplitude of the input waveform. This quasi-linearization must be carried out for a specific family of input waveforms. An example might be the family of sine-wave inputs; in this case the system would be characterized by an SIDF or sine input describing function $H (A,ω)$ giving the system response to an input consisting of a sine wave of amplitude A and frequency $ω$ . (This SIDF is a generalization of the transfer function $H (ω)$ used to characterize linear systems). Other types of describing functions that have been used are DF's for level inputs and for Gaussian noise inputs. While not a complete description of the system, the DF's often suffice to answer specific questions about control and stability.