A Nonlinear Fractional - Order $\mathcal{H}_{\infty}$∞ Observer Design for the State of Charge Estimation of Lithium-Ion Electric Vehicle Batteries

The accurate estimation of the state of charge (SOC) in Lithium-Ion batteries (LIBs) holds paramount importance within the battery management system (BMS) for electric vehicles (EVs). The utilization of fractional order models (FOMs) derived from frequency-domain modeling has emerged as a noteworthy approach, offering unique insights into the intricacies of SOC estimation. In this study, a fractional order equivalent circuit model (FOECM) based on electrochemical impedance spectra (EIS) of LIB is considered, based on the model an $\mathcal{H}_{\infty}$∞ observer is designed for battery SOC estimation by utilizing a continuous frequency distributed model (CFDM) representation of the fractional system and Lyapunov-Krasovskii functional (LKF) approach. In the end, the effectiveness of the proposed observer is confirmed through validation using a numerical example.