Abstract
An indirect downsampling approach for continuous-time input/output system identification is proposed. This modus operandi was introduced to system identification through a sub-space algorithm, where the input/output data set is partitioned into lower rate m subsets. Then, a state-space discrete-time model is identified by fusing the data subsets into a single one. In the present work the identification of the input/output downsampled model is performed by a least squares and a simplified refined instrumental variables (IV) procedures. In this approach, the inter-sample behaviour is preserved by the addition of fictitious inputs, leading to an increase of excitation requirements of the input signal. This over requirement is removed by directly estimating from the data the parameters of the transfer function numerator. The performance of the method is illustrated using the Rao-Garnier test system.

Abstract
Li-ion batteries are widely used in electric vehicles, grid storage, and portable electronics. Battery Management Systems play a crucial role in ensuring the safety, efficiency, and longevity of Li-ion batteries. Accurate battery modelling is essential for effective battery management functionality, enabling precise state of charge/ state of health estimation, as well as protection against hazardous conditions such as overcharging or overheating. This article explores system identification techniques for battery modelling using a piecewise LTI approach where separate LTI models are identified for different state of charge intervals. A modified Thevenin circuit is employed, where the open-circuit voltage is represented by a capacitor that models the bulk charge storage. The capacitance of this element is dependent on the state of charge, reflecting the nonlinear nature of the battery's charge storage mechanism. Additionally, parallel resistor-capacitor networks capture transient voltage recovery dynamics. The identification process estimates the battery parameters from experimental data, and the resulting piecewise models are interpolated using cubic splines to construct a linear parameter-varying (LPV) representation of the system. The proposed methodology was validated through experimental results, demonstrating its effectiveness in enhancing battery management performance. Namely, (i) the model accurately captures the battery's voltage response with minimal error. (ii) the LPV model obtained by fitting splines to the estimated parameters demonstrates a level of accuracy comparable to that of the piecewise LTI model. (iii) the model robustness was validated through a continuous discharge test, showing strong agreement with experimental data and, therefore, demonstrating its reliability in real-world operating conditions. These results highlight the potential of the proposed methodology in improving battery management systems. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)