Stability analysis and controller design for a linear system with Duhem hysteresis nonlinearity

In this paper, we investigate the stability of feedback interconnections between a linear system and a Duhem hysteresis operator, where the linear system satisfies either counter-clockwise (CCW) or clockwise (CW) input-output dynamics [1], [13]. More precisely, depending on the input-output dynamics of each system, we present sufficient conditions on the linear system that guarantee the stability of the closed-loop systems. Based on these results we introduce a control design methodology for stabilizing a linear plant with a counterclockwise Duhem hysteresis operator.