This work studies the estimation of internal states and voltages in a battery pack composed by lithium-ion cells subject to limited voltage and temperature measurements. A reduced-order electrochemical model for each cell is used. The considered cells are heterogeneous. They are electrically interconnected in series and thermally coupled. The resulting model is linearized and reformulated as a descriptor system. Such a model provides a unified modeling framework accounting for both battery cell dynamics and algebraic states arising from standard Kirchhoff’s laws. An observability study is exploited to design an observable descriptor system that requires the measurement of the surface temperature of one cell together with the total voltage. We resort to Lyapunov theory and the algebraic relationship between the descriptor system states and the measurements to derive a state observer that meets the following conditions. The error system is input-to-state stable and the effect of cell-to-cell variations on a specified performance variable is minimized. The state observer is obtained by solving a set of LMIs. The proposed scheme is able to estimate the state of each individual cell, including state of charge and inner temperature, as well as the unmeasured voltages. The effectiveness of the approach is tested in simulation.

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