An islanded AC microgrid (MG) operates independently from the main grid, and delivers power to a localized area through distributed energy resources (DERs). Effective power management and control strategies, like droop control, are essential for balancing supply and demand, particularly under variable load conditions in an islanded microgrid (IMG). Droop control can be communication-based or non-communication-based. In Non-communication-based droop control methods, droop gains and control gains are obtained by minimizing voltage, real power, and reactive power deviations over a limited set of operating conditions, but in a practical system, numerous operating conditions are possible. On the other hand, communication-based methods track generation and load changes to update droop gains and control gains but face challenges like noise, signal loss, delays, and cyber-attacks. This work uses DG voltage, loads, frequency, and real and reactive power as a range/interval to consider uncertainty. An interval state space model is developed for IMG. The interval state matrix incorporates all the possible operating conditions. An objective function is formulated which is solved by particle swarm optimization (PSO). The proposed method is implemented on a test system and simulation results compared with a multi-objective evolutionary algorithm based on decomposition (MOEA/D) called centripetal force-gravity search algorithm (CF-GSA) method that is based on communication. The simulation results demonstrate that the proposed method performs as good as MOEA/D method, but without the need for communication.