This paper proposes a decentralized control strategy for the voltage regulation of islanded inverter-interfaced micro- grids. We show that an inverter-interfaced microgrid under plug- and-play (PnP) functionality of distributed generations (DGs) can be cast as a linear time-invariant (LTI) system subject to polytopic-type uncertainty. Then, by virtue of this novel description and use of the results from theory of robust control, the microgrid control system guarantees stability and a desired performance even in the case of PnP operation of DGs. The robust controller is a solution of a convex optimization problem. The main properties of the proposed controller are that 1) it is fully decentralized and local controllers of DGs use only local measurements, 2) the controller guarantees the stability of the overall system, 3) the controller allows plug-and-play functionality of DGs in microgrids, 4) the controller is robust against microgrid topology change. Various case studies, based on time- domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed control strategy in terms of voltage tracking, microgrid topology change, plug-and-play capability features, and load changes.