Structural vibration control via passive electrical shunting and active (hybrid) actuation of a piezoceramic wafer bonded onto the surface of a simply supported beam is investigated with emphasis on modeling and understanding the effect of piezoceramic nonlinearity on system performance. A nonlinear rate-independent hysteresis model, the Ishlinskii hysteresis (IM) model, is experimentally identified for the PZT wafer by itself and then integrated into the coupled dynamic equations of the overall system consisting of the beam and electrically shunted PZT wafer. Experimental studies of the system validate the theoretical model. This model is then used to investigate the impact of PZT hysteresis on its vibration control performance in passive and hybrid scenarios that have been optimized based on a linear system assumption. A multi-term describing function representation of the IM hysteresis model is formulated to aid in computational studies.