Haptic rendering denotes the process of computing and displaying forces from a virtual environment to a human operator via a haptic device. From the control point of view, the haptic system comprising virtual environment, haptic device, and human operator is a hybrid control system that contains both discrete- and continuous-time elements. Discrete-time sampling as well as time delay that is typically present in such haptic systems may lead to unstable behavior. This thesis investigates stability, passivity, and control design of such hybrid system. Its primary goal is to close some of the existing lacks in the current state of research, in particular to analyze the influence of the human operator on a haptic system behavior, to investigate the precise effect of delay and discrete-time sampling, and to introduce optimal control methods to the field of haptic rendering.