State Space Mathematical Modeling and State of Charge Estimation of 18650 Panasonic Li-Ion Battery Using $\mathcal{L}_{2}-\mathcal{L}_{\infty}$ Observer Design

This study focuses on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{2}-\mathcal{L}_{\infty}$</tex> observer design, which aims to enhance the accuracy of State of Charge (SOC) estimation in a 2RC (two resistor-capacitor) Li-Ion battery (LIB) model. Validation was performed using Hybrid Pulse Power Characterization (HPPC) for Panasonic (NCR-18650B) cells. The observer's goal is to accurately estimate the battery condition despite various uncertainties and disruptions, utilizing Lyapunov methods and linear matrix inequality (LMI) techniques. It employs observer gain to reduce disturbances and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{2}-\mathcal{L}_{\infty}$</tex> norms to ensure minimal error in steady-state performance. Integrating this observer allows the model to more accurately capture the battery's dynamic behavior, resulting in improved state estimation and reliable insights into battery performance under various operating conditions.