Prosthetic hands are important tools for improving the lives of upper limb amputees, yet most devices lack the ability to provide a sense of touch back to the user. Recent improvements have been made in electromyography (EMG) prosthesis control as well as in biologically relevant tactile sensors to provide sensory feedback to amputees through nerve stimulation. However, sensory feedback has been designed heuristically, which can lead to either unnatural sensations or to excessive feedback that bothers the user. In this study, we apply optimal control techniques to synthesize sensory feedback to the user, and to synthesize the conversion from EMG to an actuation command to the prosthesis. Specifically, we construct a feedback control system architecture and solve the H_∞ model matching problem to make the closed-loop user-prosthetic system to behave like a pre-specified ideal system in response to elemental inputs (e.g. impulse, step, etc). We design feedback controllers assuming that human and prosthetic components behave in a linear fashion as a proof-of-concept, and the closed-loop system is able to match ideal systems that are slow, fast and that have both slow and fast dynamics (like healthy humans).