On the Characterization of the Duhem Hysteresis Operator with Clockwise   Input-Output Dynamics
  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. 
Ruiyue Ouyang, Vincent Andrieu, Bayu Jayawardhana
math.OC cs.SY