H_∞ Observer Based on Descriptor Systems Applied to Estimate the State of Charge

This paper proposes an H∞ observer based on descriptor systems to estimate the state of charge (SOC). The battery's open-current voltage is chosen as a generalized state variable, thereby avoiding the artificial derivative calculation of the algebraic equation for the SOC. Furthermore, the observer's dynamic performance is saved. To decrease the impacts of the uncertain noise and parameter perturbations, nonlinear H∞ theory is implemented to design the observer. The sufficient conditions for the H∞ observer to guarantee the disturbance suppression performance index are given and proved by the Lyapunov stability theory. This paper systematically gives the design steps of battery SOC H∞ observers. The simulation results highlight the accuracy, transient performance, and robustness of the presented method.