A distributed control of a Microgrid (MG) depends on the Communication Network (CN) for the exchange of information among the Distributed Generators (DGs). Most of the existing control schemes consider ideal communication among the DGs however, in practical systems, delays are inherited that can affect the dynamic performance and even destabilize an MG. Therefore, in this research work, a distributed secondary controller for an islanded MG is designed considering communication delays. Sufficient delay-independent conditions for robust stability of the buffer free distributed averaging proportional integral control scheme are proposed. Both small and large time varying communication delays are analysed using Lyapunov Krasovskii and Lyapunov Razumikhin’s approach. A sensitivity analysis is performed to demonstrate the system's stability. Finally, the efficacy of the controller is demonstrated through simulation studies.