I. Introduction
RECENTLY, piezo-actuated stage has many effective applications in ultra-high precision positioning systems [2] [3] [6] [7] [8] [10]. The piezo electric actuator (PEA) is used to meet the requirement of nanometer resolution in displacement, high stiffness and rapid response. However, the main disadvantage of PEA is the hysteresis phenomenon between the applied electric voltage and the displacement. Due to the undifferentiable and nonmemoryless character of the hysteresis, it causes position errors which limit the operating speed and precision of the PEA. The development of control techniques to mitigate the effects of hysteresis has been studied for decades and has recently re-attracted significant attention [8]. Interest in studying dynamic systems with actuator hysteresis is motivated by the fact that they are nonlinear system with nonsmooth nonlinearities for which traditional control methods are insufficient and thus require development of alternate effective approaches. Development of a control frame for the piezo-actuated stage is quite a challenging task.