State-of-Charge Estimation for Lithium-Ion Batteries Under Noisy and Sampled Output Measurements

This paper deals with the problem of state-of-charge estimation for lithium-ion batteries under sampled and noisy terminal-voltage measurements. To address this problem, a robust continuous–discrete observer is proposed for a first-order Thevenin battery model, allowing continuous estimation of the state of charge and the RC polarization voltage even when the output is only available at discrete time instants. The observer gain is obtained through a linear matrix inequality (LMI)-based design aimed at reducing the influence of measurement noise. Sufficient conditions ensuring the convergence of the observer are derived. The stability analysis shows that the observation error converges exponentially to a bounded region around the origin, whose size depends on the measurement-noise bound and the maximum sampling interval. In the noise-free case, exponential convergence to the origin is recovered. Moreover, an explicit condition on the maximum allowable sampling interval is obtained. The proposed approach is evaluated through numerical simulations and experimental tests under different sampling intervals and noise conditions. Finally, the LMI-based gain design is compared with a conventional pole-placement approach, showing lower sensitivity to measurement noise while maintaining satisfactory state-estimation performance.