This chapter provides the fundamental theoretical framework upon which the next chapters expand in different directions. Herein, a distributed constrained control scheme for meshed DC microgrids is formulated, taking into consideration both local constraints on the power generation components and coupled constraints between the interactions of network agents. A rigorous analysis is performed to provide sufficient conditions under which a receding horizon approach is able to guarantee asymptotic convergence to a desired equilibrium point. At the same time, sufficient conditions are also provided to show system robustness to unknown constant power load demand perturbations and guarantee that the desired operational constraints are satisfied both during transient and steady-state performance. The next pages characterise a region of the state space and the maximum load demand such that the control scheme remains recursively feasible at all times.