Class Of Hysteresis Operators Research Articles

Uniqueness and decay estimates for a class of parabolic partial differential equations with hysteresis and convection

Abstract We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators.

Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions

An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators under consideration contains many standard hysteresis nonlinearities which are important in control engineering such as backlash (or play), plastic-elastic (or stop) and Prandtl operators. Whilst the main results are developed in the context of integral equations of convolution type, applications to well-posed state space systems are also considered.

On a class of multi-dimensional Prandtl–Ishlinskii operators

In this paper, a class of multi-dimensional hysteresis operators of generalized Prandtl–Ishlinskii form is introduced which can be viewed as a possibility to extend the famous one-dimensional Preisach model of hysteresis to higher space dimensions. We study the continuity properties of these hysteresis operators and of the hysteresis potential operators associated with them. It is also indicated, how this class of hysteresis operators can be applied to a class of phase-field systems occurring in the theory of phase transitions with non-conserved order parameters.