The design and stability analysis of bidirectional DC–DC converters play a crucial role in ensuring efficient and reliable power flow between the energy sources and storage systems. This research introduces an innovative approach by integrating state-space techniques with advanced control strategies to enhance the performance and stability of bidirectional converters. The proposed framework focuses on key operational modes on charging and discharging while employing Pulse Width Modulation (PWM) for the precise voltage and current regulation. By leveraging state-space analysis, the study ensures that the converter maintains predictable and stable operation under varying load and input conditions. MATLAB simulations validate the proposed design, demonstrating superior dynamic performance and robustness.