Grid-connected Voltage Source Converters (VSCs) are widely used in Power Electronic-based (PE-based) power systems. Therefore, it is necessary to have stability analysis tools for different system conditions. In this paper, Lyapunov- and eigenvalue-based methods are used in order to analyze the stability of the grid-connected VSC. This Lyapunov-based technique is valid for large-signal stability analysis, when the system is subjected to a large disturbance. Eigenvalue-based methods are simpler but these are not valid under large disturbance conditions. The Lyapunov-based analysis can systematically model the linear and non-linear behavior of the grid-connected VSCs.