In the islanded mode operation of a microgrid, a part of the distributed network becomes electrically separated from the main grid, while loads are supported by local sources. Such distributed energy sources (DERs) are typically power electronic based, making the full system complex to study. A method for analyzing such a complicated system is discussed in this paper. A microgrid system with two inverters working as DERs is proposed. The controllers for the inverters are designed in the dq reference frame. Nonlinear equations are derived to reflect the system dynamics. These equations are linearized around steady-state operating points to develop a state-space model of the microgrid. An averaged model is used in the derivation of the mathematical model that results in a simplified system of equations. An eigenvalue analysis is completed using the linearized model to determine the small-signal stability of the system. A simulation of the proposed microgrid system consisting of two inverter based DERs, passive loads, and a distribution line is performed. An experimental testbed is designed to investigate the system's dynamics during load perturbation. Results obtained from the simulation and hardware experiment are compared with those predicted by the mathematical model to verify its accuracy.