Bus voltage stability is a key issue in future medium-voltage DC (MVDC) power systems on ships. The presence of high-bandwidth controlled load converters (Constant Power Load, CPL) may induce voltage instabilities. A control design procedure is presented which starts at the modeling level and comes to control implementation. A control method based on a Linearization via State Feedback (LSF), is proposed to face the CPL destabilizing effect and to ensure the MVDC bus voltage stability. A multiconverter shipboard DC grid is analyzed by means of a new comprehensive model, which is able to capture the overall behavior in a second-order nonlinear differential equation. Exploiting DC-DC converters that interface power sources to the bus, LSF technique is able to compensate for system nonlinearities, obtaining a linear system. Then, traditional linear control techniques can be applied to obtain a desired pole placement. With reference to system parameters mismatch, LSF control design is verified by means of a sensitivity analysis, evaluating the possibility of an over-linearization strategy. Time-domain numerical simulations are used to validate the proposed control, in presence of relevant perturbations by means of a two-way comparison (average value model and detailed switching model).