Effect of the shape demagnetizing field on the stability of the Preisach diagram

In this paper it is proven that, in general, the shape-demagnetizing-field transformation breaks, or modifies, the stability of the Preisach diagram PD. The proof is based on the Mayergoyz's theorem. A new theorem which gives the necessary and sufficient conditions for the invariance of such a stability is also proven. Moreover, a rigorous mathematical base for feedback generalizations of the Preisach model PM is given. These results are relevant not only for a proper interpretation of magnetic hysteresis measurements, but also, more generally, for the mathematical modelling of any kind of hysteretic system regardless of the physical origin of hysteresis nonlinearities.