Along with the rapid growth in green energy utilization, microgrids are becoming an interesting part of the future power systems. This paper presents a transient trajectory optimization of parallel connected inverter system in an islanded microgrid. Optimal state and control transient trajectories are generated which drive each individual inverter from given initial conditions to their respective desired steady state equilibrium. This trajectory optimization is performed in decentralized manner and they are the open loop, local optimal control signals of the inverters. The Pontryagin's minimum principle is employed to obtain the optimal state and control signal trajectories. Then, a stability analysis of the system with the local optimal control signals is done by a Lyapunov approach. Dynamic model of the system and the optimum trajectories are obtained in the d-q reference frame. Two example microgrid systems, one with three inverters and the other one with five inverters, were used to demonstrate the effectiveness and performance of the proposed approach which can be easily extended to any type of microgrid such as AC, DC, hybrid microgrids in both islanded or grid connected mode.