This thesis contributes to the modeling and analysis of longitudinal radio frequency (RF) feedback systems in heavy-ion synchrotrons. Synchrotrons are ring accelerators with a constant reference orbit of the particle beam. They allow the acceleration of particles such as electrons, protons, and heavy ions to highest energies. The desired specifications for beam properties such as the quality, energy, and intensity drive the development of new accelerator components. Among other objectives, the stabilization of the beam before and during the acceleration is desirable to preserve the beam quality. The thesis deals with the modeling of longitudinal coherent oscillations of a bunched beam. The main focus is on the usability of the models for the analysis and design of digital RF feedback loops. The analysis of these models with methods from control theory leads to new insight into the possibilities of RF feedback with regard to the longitudinal beam stabilization. In particular it is shown that the nonlinearity of the beam dynamics plays a major role in the damping of coherent oscillations of higher order. An analysis of a specific RF feedback setup and the comparison with experimental data shows the practical relevance of the models.