In this paper, we propose an algorithm to solve the balancing problem of multi-cell battery systems consisting in the equalization of all cells state of charge (SoC). A nonlinear cell model is presented and experimental LiFePO4 battery cell parameters are used. By considering the main cell nonlinear dynamics, ultimate balancing is guaranteed via state feedback. Output feedback versions of the proposed balancing algorithm based on Kalman filtering are evaluated via numerical simulations using the identified model. For the case when the SoC is not available and, in addition, the cell parameters are unknown, a novel SoC/parameter joint estimator is developed for a class of nonlinear cells via amplitude demodulation and online normalized least squares estimation techniques.