In this paper, a robust decentralized controller is designed for automatic voltage regulator (AVR) and load frequency control (LFC) systems of a generator in an islanded microgrid with multiple distributed generation systems. This control strategy can be readily applied to an islanded microgrid which consists of renewable distributed generation and energy storage systems. The control strategy proposed in this paper includes multiple local droop controllers, as well as robust decentralized controller that are designed and optimized independently by using the μ-synthesis technique. These controllers account for the dynamic coupling among the areas of the islanded microgrid without any communication links required among the local controllers. Moreover, these controllers are designed to be robust to the variations of different parameters of the microgrid, and hence improve the voltage and frequency control performance significantly. Simulation results of a small microgrid with a generator and a renewable energy resource confirm the effectiveness of the controller design approach proposed in this paper.