The study in this paper is motivated by the modeling of control valves with significant stiction. By assuming linear dynamics of the controlled process, the joint characterization of the control valve and of the controlled process is formulated as the identification of an extended Hammerstein system. A point-slope-based hysteresis model is used to describe the input hysteresis nonlinearity of the control valve. An iterative algorithm is proposed to solve the identification problem. The basic idea is to separate the ascent and descent paths of the input hysteresis nonlinearity subject to oscillatory excitations. Some identifiability analysis is performed: the proposed extended Hammerstein model structure is identifiable, and given the true input nonlinearity, the oscillatory signals in feedback control loops are shown to be informative by exploiting the cyclo-stationarity of these oscillatory signals. Industrial examples are provided to verify the effectiveness of the proposed identification algorithm in characterizing complicated characteristics of control valve stiction in practice.