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I can add some more details but only with german references. Can this be accepted?-- hfst~~ —Preceding unsigned comment added by Hfst ( talk • contribs) 21:53, 16 February 2009 (UTC)
I think it would be correct to add something about justifications and limitation of application of DFM:
The describing function method (DFM, which is also known as harmonic balance method), is a widely used approximate method (that is, not rigorously mathematically substantiated) of searching for oscillations which are close to the harmonic periodic oscillations of non-linear dynamical systems. But it is well known that DFM can lead to incorrect results. Such examples for the first time have been presented by Tzypkin in a bang-bane systems (Tsypkin Ya.Z., Relay Control Systems. Cambridge: Univ Press; 1984).
Also, in the case when conditions of Aizerman's or Kalman conjectures are fulfilled, there is no periodic solutions by DFM, but counterexamples with periodic solutions are well known (Bragin V.O., Vagaitsev V.I., Kuznetsov N.V., Leonov G.A., Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits, Journal of Computer and Systems Sciences International, 2011, Vol. 50, No. 4, pp. 511-543; Aizerman's and Kalman's conjectures and DFM).
![]() | This article is rated Stub-class on Wikipedia's
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I can add some more details but only with german references. Can this be accepted?-- hfst~~ —Preceding unsigned comment added by Hfst ( talk • contribs) 21:53, 16 February 2009 (UTC)
I think it would be correct to add something about justifications and limitation of application of DFM:
The describing function method (DFM, which is also known as harmonic balance method), is a widely used approximate method (that is, not rigorously mathematically substantiated) of searching for oscillations which are close to the harmonic periodic oscillations of non-linear dynamical systems. But it is well known that DFM can lead to incorrect results. Such examples for the first time have been presented by Tzypkin in a bang-bane systems (Tsypkin Ya.Z., Relay Control Systems. Cambridge: Univ Press; 1984).
Also, in the case when conditions of Aizerman's or Kalman conjectures are fulfilled, there is no periodic solutions by DFM, but counterexamples with periodic solutions are well known (Bragin V.O., Vagaitsev V.I., Kuznetsov N.V., Leonov G.A., Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits, Journal of Computer and Systems Sciences International, 2011, Vol. 50, No. 4, pp. 511-543; Aizerman's and Kalman's conjectures and DFM).