In this thesis, a Lyapunov-based method for analyzing the stability of a switched microgrid system is proposed. First, a small second-order system is explored as example to demonstrate the effectiveness of switching patterns on the stability of a system switching among different respectively stable operating points. Lyapunov function is employed in order to determine the proper state-based switching conditions under which global stability is guaranteed, or under which the system is driven unstable. Then, a linearized state-space model of a looped seven-node microgrid is established. Solid-state transformers (SSTs), distributed energy storage devices and synchronous generators are introduced and modeled in this system. The model uses accurate SST models to highlight the different performance in terms of stability between traditional power grid system and distributed microgrid system. Also, a control method is employed to ensure static stability. Based on this model, the system transfer matrix is derived and used in the Lyapunov function computation numerically. Finally, a high order system switching function is derived. The switching function is a state-based hypersurface. System stability may be ensured by switching the load or power command when the operating point cross the switching function. Conversely, system instability may be ensured with a different switching function. Finally, the approach is verified using MATLAB simulations.