Voltage-source converters (VSCs) are receiving widespread acceptance as the enabling technology to integrate renewable energy sources, energy storage units, and modern dc-type loads into existing ac grids via multiterminal dc grids. Droop control is a common power-sharing strategy to facilitate autonomous power sharing among different terminals in dc grids. However, the dynamics and stability of a gird-connected VSC with dc power sharing droop control can be affected by several important factors that are not addressed in the current literature. Important among these are: 1) ignoring the effect of the outer droop loop on the dc-link voltage dynamics when the dc-link voltage controller is designed; 2) uncertainties in the dc grid parameters; and 3) disturbances in the dc grid (i.e., power absorbed or injected from/to the dc grid). To overcome these difficulties, this paper presents a robust power sharing and dc-link voltage regulation controller for grid-connected VSCs in dc grids applications. A detailed dynamic model that considers the droop controller dynamics and the impact of the effective dc-side load parameters and disturbances imposed on the VSC is developed. Then, a robust controller that preserves system stability and robust performance is developed. A mathematical analysis, as well as simulation and experimental results, are provided to show the effectiveness of the proposed controller.