In this talk, I discuss the dissipativity property of Duhem hysteresis models which is related to the property of counter-clockwise (CCW) and clockwise (CW) systems. Under mild assumptions on the functions which define the Duhem model, an explicit construction of the storage functions is given based on the data on these functions. The constructed storage function is also related to the underlying anhysteresis function which has been used to describe hysteresis in magnetic material.
In the second part of the talk, we investigate the stability of a feedback interconnection between a linear system and a Duhem hysteresis operator, where the linear system and the Duhem hysteresis operator satisfy either the counter-clockwise (CCW) or clockwise (CW) input-output dynamics. More precisely, we present sufficient conditions for the stability of the interconnected system that depend on the CW or CCW properties of the linear system and the Duhem operator. Based on these results we introduce a control design methodology for stabilizing a linear plant with a hysteretic actuator or sensor without requiring precise information on the hysteresis operator.
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