The complexity of power networks is increasing rapidly due to the growing use of power electronic devices and the expansion of new energy sources. As a result, ensuring the stability of power systems has become increasingly important. Grid-connected inverter systems play a crucial role in modern power systems, and studying their stability can aid in developing new tools for stability analysis. Transient stability assessment (TSA) involves analyzing the behavior of system variables during and after disturbances. It's preferred to express stability boundaries as nonlinear functions of system variables, which traditional analytical methods struggle to achieve. In recent decades, Machine Learning (ML) techniques have been proposed. However, most studies focus on synchronous generator-based systems, utilizing physical data such as power flow, voltage, and current. In addition to using physical quantities, the stability status of the entire power system can be determined by either the state variables or a subset thereof. This thesis introduces an analysis method based on statistical method and machine learning to determine the stability status of the inverter connected to the gird. The analysis method focuses on the examination and selection of appropriate state variables in inverter that can be used for rapid and accurate predict the stability. The dataset was generated by simulating disturbances and capturing the variables at the disturbance's clearance and the multiple simulations of a modified 12-bus system using the electromagnetic transient simulation tool, PSCAD/EMTDC. The research framework, established through a detailed literature review, includes describing the test system and modifications for inverter-based system. It explores gird-following inverter modeling and uses statistical methods for effective transient stability assessment.. The decision tree classifier is the machine learning approach utilized in this research. The constructed classifier correlates variables with system stability, reducing the required variables for TSA without compromising accuracy. The variables in outer reactive power control, q-axis current control, and phase locked loop exhibit notable correlation with system stability. This study contributes to proposes a methodology to identify a subset of state variables in inverters that significantly influence transient stability, and this identified subset is then utilized to assess the stability.