On the Characterization of the Duhem Hysteresis Operator with Clockwise Input-Output Dynamics

TL;DR

This paper analyzes the dissipativity and stability of a class of Duhem hysteresis operators with clockwise input-output behavior, providing conditions for CW property and a storage function, applied to hysteretic friction models.

Contribution

It offers explicit conditions and a construction for the storage function of CW Duhem hysteresis operators, linking theoretical properties to stability analysis.

Findings

Duhem operator can be CW under specific conditions

Explicit storage function construction for CW systems

Stability of a second order system with hysteretic friction

Abstract

In this paper we investigate the dissipativity property of a certain class of Duhem hysteresis operator, which has clockwise (CW) input-output (I/O) behavior. In particular, we provide sufficient conditions on the Duhem operator such that it is CW and propose an explicit construction of the corresponding storage function satisfying dissipation inequality of CW systems. The result is used to analyze the stability of a second order system with hysteretic friction which is described by a Dahl model.