  The state of charge (SOC) of lithium-ion batteries needs to be accurately
estimated for safety and reliability purposes. For battery packs made of a
large number of cells, it is not always feasible to design one SOC estimator
per cell due to limited computational resources. Instead, only the minimum and
the maximum SOC need to be estimated. The challenge is that the cells having
minimum and maximum SOC typically change over time. In this context, we present
a low-dimensional hybrid estimator of the minimum (maximum) SOC, whose
convergence is analytically guaranteed. We consider for this purpose a battery
consisting of cells interconnected in series, which we model by electric
equivalent circuit models. We then present the hybrid estimator, which runs an
observer designed for a single cell at any time instant, selected by a
switching-like logic mechanism. We establish a practical exponential stability
property for the estimation error on the minimum (maximum) SOC thereby
guaranteeing the ability of the hybrid scheme to generate accurate estimates of
the minimum (maximum) SOC. The analysis relies on non-smooth hybrid Lyapunov
techniques. A numerical illustration is provided to showcase the relevance of
the proposed approach.
