In this paper, the generalized Prandtl-Ishlinskii model is used to design an adaptive controller for a class of nonlinear systems which contain hysteresis phenomenon within their dynamic equation as a function of state variables. The controller design is carried out through adaptive backstepping approach and the stability proof is given based on Lyapunov stability theory. In contrast to the systems in which hysteresis appear in their input, the inverse based methods cannot be applied to systems with hysteresis in their states. The proposed controller is able to cope with different kinds of hysteresis nonlinearity (saturated and unsaturated). Finally, to show the effectiveness of the proposed method, simulations are carried out for a second order “mass–nonlinear spring–damper” system.

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