Abstract: The performance of smart structures in trajectory tracking under sub-micron level is hindered by the stress-dependent hysteresis generated by varying mechanical loads. In this paper, a stress-dependent Preisach operator is proposed for describing the hysteresis nonlinearity under both varying input current and compressive stress featured by introducing the dependence of the density function on the compressive stress. Subsequently, the properties together with the parameter identification scheme based on a fuzzy tree method of the presented operator are investigated to formulate an inverse compensator. Then, a feedback control scheme combined with a feed-forward compensator is implemented to a magnetostrictive smart structure (MSS) for real-time precise trajectory tracking. Compared with the classical operator, the proposed operator and corresponding control scheme experimentally demonstrate a dramatically improved performance for mitigating the effects of stress-dependent hysteresis.