Comment on: A robust observer based on the nonlinear descriptor systems application to estimate the state of charge of lithium-ion batteries

In the paper by Meng et al. (2023), an observer is proposed for nonlinear singular systems. The authors claim that their method effectively handles nonlinearity and disturbances affecting both the dynamic and algebraic parts of the system. They compare the performance of their observer with that proposed by Darouach et al. (2011), focusing on observer design for nonlinear singular systems with disturbances affecting the dynamic and algebraic parts as well as the output of the system. Furthermore, this approach has been extended to several other classes of systems, as discussed in Zerrougui et al. (2014) [1], Darouach et al. (2013) [2], and Darouach et al. (2010) [3]. Meng et al. apply their observer to estimate the state of charge of a lithium battery in comparison with the results in Snoussi et al. (2020). In this note, we aim to highlight the discrepancies between our respective findings. Specifically, we explain that the observer proposed by Meng et al. (2023), is more restrictive and may not be suitable for singular systems with nonlinear algebraic components or disturbances affecting this part or affecting outputs. Additionally, Meng et al. (2023) revisit the framework introduced in Darouach et al. (2011), adding a particular form for the matrix $\Phi$ that renders it more restrictive, without any contribution in the stability synthesis part.