We develop a control-theoretic analysis of a brain-machine interface (BMI)-based neuroprosthetic system for voluntary single joint reaching task in the absence of visual feedback. Using synthetic data obtained through the simulation of an experimentally validated psycho-physiological cortical circuit model, an adapted Weiner filter based linear decoder is developed. We analyze the performance of the decoder in the presence and the absence of natural proprioceptive feedback information. Through simulation, we show that the decoder performance degrades significantly in the absence of the natural proprioception. Finally, an optimal artificial sensory feedback is designed in the receding horizon control framework to stimulate appropriate cortical sensory area neurons. Our results show the recovery of natural performance of the reaching task during the online operation of the designed BMI.