Abstract
This paper presents a formal mathematical treatment of the general properties of scalar hysteretic systems. A generalization of the Preisach representation including both irreversible and reversible components of magnetization is given. It is shown that the Mayergoyz’s theorem has a more general validity in this new representation. The effect of a linear feedback transformation on the existence of the generalized Preisach representation is considered, and the necessary and sufficient conditions for the invariance of such an existence are given. Finally the effect of the shape demagnetizing field on the relative weight of reversible and irreversible components of magnetization is discussed. The reversible component is found to be enhanced by the shape demagnetizing field. The results obtained in this paper are relevant not only for magnetic systems, but also for the mathematical modelling of any kind of hysteretic system.
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