We consider multirate sampled-data output feedback control of smart material actuated systems where the measurement sampling rate is made faster than the control update rate. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. We show that the sampled-data output feedback controller achieves stabilization with respect to a closed set in the presence of hysteresis modeling uncertainty. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.