In this paper, we address the problem of voltage stability and power sharing in DC microgrids with time-varying power demand. By exploiting the monotonicity property enjoyed by the system, and under the assumption of full observ-ability of the bus voltages, we design a centralized, abstraction-based symbolic controller that, once refined into a controller for the original system, ensures the required specifications. Whereas load voltages cannot be measured, we propose an appropriate decomposition of the system, such that the control problem can be reformulated in terms of assume-guarantee contracts to be satisfied by the observable and unobservable components. A constructive procedure to determine suitable contracts is further investigated and the obtained results are validated with two numerical examples.