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This work is focused on the state of charge (SOC) estimation of a lithium-ion battery based on a nonlinear observer. First, the second-order resistor-capacitor (RC) model of the battery pack is introduced by utilizing the physical behavior of the battery. Then, for the nonlinear function of the RC model, a one-sided Lipschitz condition is proposed to ensure that the nonlinear function can play a positive role in the observer design. After that, a nonlinear observer design criterion is presented based on the H ∞ method, which is formulated as linear matrix inequalities (LMIs). Compared with existing nonlinear observer-based SOC estimation methods, the proposed observer design criterion does not depend on any estimates of the unknown variables. Consequently, the convergence of the proposed nonlinear observer is guaranteed for any operating conditions. Finally, both the static and dynamic experimental cases are given to show the efficiency of the proposed nonlinear observer by comparing with the classic extended Kalman filter (EKF).

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