Discrete-time Luenberger observer design for Lithium-ion battery state-of-charge with stability guarantee

State-of-charge (SOC) estimation is particularly important as it provides information about the remaining energy capacity of the battery, allowing for better planning and utilization. Accurate SOC estimation is challenging because it can-not be directly measured from the battery. Instead, it is estimated by analyzing measurable variables such as current and voltage. To address this challenge, a discrete-time observer-based SOC estimation approach is proposed in this paper. This approach utilizes a second-order equivalent circuit model and a piecewise linear approximation to represent the relationship between SOC and open circuit voltage (OCV). The proposed observer-based approach utilizes these models to estimate the SOC with assured asymptotic stability under specific assumptions to simplify the design process. Simulations in Python are conducted to eval-uate the performance of the designed observer. In the simulations, the SOC estimation under various conditions, such as model uncertainty, disturbances, and measurement noise, is also covered. In addition, three different observer gains are considered in the simulations. Lastly, simulation studies indicate that the estimated SOC values converge to the real SOC values, with some different behavior depending on the regarded situations.