Due to their compatibility with renewable and distributed generation, microgrids are a promising operational architecture for future power systems. Here we consider the operation of DC microgrids that arise in many applications. We adopt a linear circuit model and propose a decentralized voltage droop control strategy that is inspired by frequency droop control in AC networks. We demonstrate that our primary droop control strategy is able to achieve fair and stable load sharing (even in presence of actuation constraints) or an economic dispatch of the generation formulated as a quadratic and linearly-constrained optimization problem on the source injections. Similar to frequency droop control, voltage droop control induces a steady-state voltage drift depending on the imbalance of load and generation in the microgrid. To compensate for this steady-state error, we consider two secondary control strategies. A purely decentralized secondary integral control strategy successfully compensates for the steady-state voltage drifts yet it fails to achieve the desired optimal steady-state injections. Next, we propose a consensus filter that requires communication among the controllers, that regulates the voltage drift, and that recovers the desired optimal injections. The performance and robustness of our controllers are illustrated through simulations. (C) 2015 Elsevier Ltd. All rights reserved.