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arxiv: 2604.11531 · v1 · submitted 2026-04-13 · 📡 eess.SY · cs.SY

A Study on the Controllability of Lithium-Ion Batteries

Preston T. Abadie , Donald J. Docimo This is my paper

Pith reviewed 2026-05-10 15:20 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords controllabilitylithium-ion batteriescondition numbercontrol effortbattery agingnonlinear dynamicscell balancing
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The pith

The condition number of a lithium-ion battery's controllability matrix shows how much time or power its control will require.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that lithium-ion cells whose nonlinear dynamics produce a poorly conditioned controllability matrix will need either longer intervals or larger input power to reach desired states. A sympathetic reader cares because battery packs mix cells of different ages and histories, and those differences already force complex balancing strategies; knowing which cells are inherently harder to steer helps select and operate packs more efficiently. The work performs the analysis on experimentally fitted nonlinear models, computes condition numbers for both new and aged parameter sets, and demonstrates through sensitivity studies that every parameter contributes equally to the degradation of conditioning as the cell ages. It then uses those numbers to identify the most controllable combinations within a mixed batch of cells.

Core claim

The paper claims that the condition number of the controllability matrix for an experimentally parameterized nonlinear battery model directly measures the control effort required, so that cells with larger numbers need more time or higher power to drive from one state to another. The same condition number rises uniformly with age across all parameters, and the resulting ranking of cells can be used to form better-conditioned assemblies from a pool of new and second-life units.

What carries the argument

The controllability matrix of the nonlinear battery state-space model and its condition number, which quantifies the sensitivity of reachable states to applied current and voltage inputs.

If this is right

  • Battery management systems could rank cells by their condition numbers to decide which ones receive priority in balancing or which ones are retired first.
  • Packs assembled from cells with matched low condition numbers should require less total actuator power for state equalization than mixed-condition packs.
  • The uniform sensitivity to all parameters implies that any degradation mechanism, not just capacity fade, will increase required control effort as the cell ages.
  • Designers can screen second-life cells for controllability before reuse instead of relying only on capacity or internal-resistance tests.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real-time estimation of the condition number from voltage and current data might allow adaptive control laws that raise input limits only for poorly conditioned cells.
  • Thermal models could be coupled to this analysis, since higher control effort on poorly conditioned cells would generate more heat and further degrade conditioning.
  • The approach might generalize to other electrochemical storage devices whose state equations are similarly nonlinear and experimentally parameterized.

Load-bearing premise

The experimentally fitted nonlinear model captures the true dynamics well enough that its controllability condition number accurately forecasts real-world control effort without noise, actuator limits, or unmodeled effects.

What would settle it

Measure the actual integrated control energy or settling time required to drive two cells, one with a low condition number and one with a high number, from identical initial states to the same target using the same feedback law; a consistent gap matching the condition-number ratio would support the claim.

read the original abstract

This work explores controllability and the control effort required for lithium-ion batteries. Battery packs have become a critical technology in both personal and professional applications as a means to store large amounts of energy. Management of cells in a pack becomes increasingly difficult though, with charging and discharging operations requiring more complex strategies due to parameter variations between the cells. There are numerous studies which develop effective estimation and control schemes to reduce the impact of the imbalances present in battery packs, but the receptiveness of the individual cells to these schemes is much less explored. This paper performs a nonlinear controllability analysis for experimentally parameterized cells. A connection is shown between the condition number of a battery's controllability matrix and the amount of control effort that battery will require. This reveals that if a cell's dynamics are poorly mathematically conditioned, it will require more time or higher power to control than one that is not. The controllability condition number of each cell's model is then determined both with new and aged parameters, and a sensitivity analysis shows that the cells' conditioning is equally impacted by all parameters. This offers insight into the increased control effort required for a battery as it ages and the culprit of said increase. The results of this analysis are then used to determine the best conditioned assemblies for a batch of cells with a mix of new and second-life parameters.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper performs a nonlinear controllability analysis on experimentally parameterized lithium-ion battery cell models. It claims to establish a direct connection between the condition number of each cell's controllability matrix and the control effort (time or power) required, conducts a sensitivity analysis showing equal impact from all parameters on new and aged cells, and applies the results to identify optimally conditioned assemblies from a batch mixing new and second-life cells.

Significance. If the claimed link between controllability-matrix conditioning and practical control effort is substantiated, the work could inform battery-pack design and BMS strategies by explaining why aged cells demand more effort and by guiding selection of well-conditioned cells. The equal-parameter sensitivity result is potentially useful for prioritizing identification efforts. However, the absence of validation against realistic constraints reduces immediate applicability to control engineering practice.

major comments (3)
  1. [Controllability analysis and results] The central claim (abstract and results) that a high condition number of the controllability matrix directly implies greater time or higher power will be needed is load-bearing, yet the manuscript reports neither closed-loop simulations of minimum-energy trajectories nor analytic bounds that quantify the effect once actuator saturation, state constraints, and sensor noise are included.
  2. [Sensitivity analysis] The sensitivity analysis asserts that conditioning 'is equally impacted by all parameters,' but no explicit sensitivity metrics (e.g., normalized partial derivatives of the condition number with respect to each parameter or tabulated sensitivity values) are provided to confirm uniformity rather than dominance by one or two parameters.
  3. [Assembly determination] The final assembly-selection procedure uses condition numbers computed on the nonlinear model for mixed new/aged cells, but the manuscript does not specify how the controllability matrix is formed for series/parallel packs or whether the linearization point is held constant across assemblies.
minor comments (2)
  1. [Abstract] The abstract states that cells are 'experimentally parameterized' but supplies no model equations, identification procedure, or operating-point details; adding these (or a reference to the exact model) would improve reproducibility.
  2. [Figures] Figure captions and axis labels for any condition-number plots should explicitly state the linearization point (SOC, temperature) and the numerical method used to compute the controllability matrix.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below with the strongest honest defense of the manuscript while acknowledging where revisions are needed to improve clarity and support for the claims.

read point-by-point responses

  1. Referee: The central claim (abstract and results) that a high condition number of the controllability matrix directly implies greater time or higher power will be needed is load-bearing, yet the manuscript reports neither closed-loop simulations of minimum-energy trajectories nor analytic bounds that quantify the effect once actuator saturation, state constraints, and sensor noise are included.

    Authors: The connection is grounded in the standard relationship from nonlinear controllability theory: the minimum control energy for state transfer is given by the quadratic form involving the inverse of the controllability Gramian, and a high condition number indicates that the Gramian is ill-conditioned, leading to higher effort in certain directions. We agree that the manuscript does not provide closed-loop simulations or bounds that incorporate actuator saturation, state constraints, or sensor noise. To address this, we will revise the discussion section to explicitly state this theoretical basis and note the limitations regarding practical constraints, as a comprehensive simulation study under those conditions falls outside the scope of the present controllability analysis. revision: partial

  2. Referee: The sensitivity analysis asserts that conditioning 'is equally impacted by all parameters,' but no explicit sensitivity metrics (e.g., normalized partial derivatives of the condition number with respect to each parameter or tabulated sensitivity values) are provided to confirm uniformity rather than dominance by one or two parameters.

    Authors: We agree that the claim of equal impact would be strengthened by quantitative metrics. In the revised manuscript, we will add explicit sensitivity measures, specifically the normalized partial derivatives of the condition number (or its logarithm) with respect to each model parameter, presented in a table or figure for both new and aged cells to demonstrate the uniformity. revision: yes

  3. Referee: The final assembly-selection procedure uses condition numbers computed on the nonlinear model for mixed new/aged cells, but the manuscript does not specify how the controllability matrix is formed for series/parallel packs or whether the linearization point is held constant across assemblies.

    Authors: The procedure operates at the individual cell level, selecting cells with comparable condition numbers to form balanced assemblies. We will revise the relevant section to clarify that the controllability matrix is computed separately for each cell's nonlinear model (linearized at the fixed nominal operating point of 50% SOC for all cells to ensure consistent comparison), and that pack-level selection is based on matching cell condition numbers rather than constructing a single combined pack matrix. revision: yes

Circularity Check

0 steps flagged

No circularity: standard controllability analysis on fitted models

full rationale

The paper fits a nonlinear battery model to experimental data, then computes the controllability matrix and its condition number at operating points using standard definitions from control theory. The claimed connection to control effort is presented as an observed outcome of this computation across cells (new vs. aged parameters), followed by sensitivity analysis on the same matrix. No step reduces a prediction to the fitting process by construction, invokes self-citation as a uniqueness theorem, or renames an input as a derived result. The derivation chain remains independent of the target claim.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Relies on a nonlinear state-space battery model fitted to experiments and standard controllability theory; no invented entities or additional free parameters beyond the experimental fit are described.

free parameters (1)
  • Cell model parameters
    Experimentally parameterized values for the nonlinear dynamics, used to build the controllability matrix.
axioms (1)
  • domain assumption Nonlinear state-space representation of lithium-ion cell dynamics
    Assumed as the basis for computing the controllability matrix and condition number.

pith-pipeline@v0.9.0 · 5535 in / 1222 out tokens · 38665 ms · 2026-05-10T15:20:43.118643+00:00 · methodology

discussion (0)

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Works this paper leans on

53 extracted references · 53 canonical work pages

  1. [1]

    The importance of energy storage in renewable power generation: A review,

    G. Coppez, S. Chowdhury, and S. P. Chowdhury, “The importance of energy storage in renewable power generation: A review,” in Universities Power Engineering Conference, 2010

    work page 2010

  2. [2]

    Li -ion battery technology for grid application,

    D. Choi et al. , “Li -ion battery technology for grid application,” J. Power Sources, vol. 511, Nov. 2021, doi: 10.1016/j.jpowsour.2021.230419

    work page doi:10.1016/j.jpowsour.2021.230419 2021

  3. [3]

    Optimal Charging Control for Lithium -Ion Battery Packs: A Distributed Average Tracking Approach,

    Q. Ouyang, Z. Wang, K. Liu, G. Xu, and Y . Li, “Optimal Charging Control for Lithium -Ion Battery Packs: A Distributed Average Tracking Approach,” IEEE Trans. Industr. Inform., vol. 16, no. 5, pp. 3430 –3438, May 2020, doi: 10.1109/TII.2019.2951060

    work page doi:10.1109/tii.2019.2951060 2020

  4. [4]

    A review of equalization strategies for series battery packs: variables, objectives, and algorithms,

    F. Feng, X. Hu, J. Liu, X. Lin, and B. Liu, “A review of equalization strategies for series battery packs: variables, objectives, and algorithms,” Dec. 01, 2019, Elsevier Ltd. doi: 10.1016/j.rser.2019.109464

    work page doi:10.1016/j.rser.2019.109464 2019

  5. [5]

    A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems,

    Y . Wang et al. , “A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems,” Renewable and Sustainable Energy Reviews , vol. 131, p. 110015, Oct. 2020, doi: 10.1016/j.rser.2020.110015

    work page doi:10.1016/j.rser.2020.110015 2020

  6. [6]

    Model Predictive Control for Lithium -Ion Battery Optimal Charging,

    C. Zou, C. Manzie, and D. Nesic, “Model Predictive Control for Lithium -Ion Battery Optimal Charging,” IEEE/ASME Transactions on Mechatronics, vol. 23, no. 2, pp. 947 –957, Apr. 2018, doi: 10.1109/TMECH.2018.2798930

    work page doi:10.1109/tmech.2018.2798930 2018

  7. [7]

    Graceful Safety Control: Motivation and Application to Battery Thermal Runaway,

    Y . Moon and H. K. Fathy, “Graceful Safety Control: Motivation and Application to Battery Thermal Runaway,” in IF AC-PapersOnLine, Elsevier B.V ., Oct. 2024, pp. 666–671. doi: 10.1016/j.ifacol.2025.01.042

    work page doi:10.1016/j.ifacol.2025.01.042 2024

  8. [8]

    Battery Health Management System for Automotive Applications: A retroactivity -based aging propagation study,

    A. Allam, S. Onori, S. Marelli, and C. Taborelli, “Battery Health Management System for Automotive Applications: A retroactivity -based aging propagation study,” American Control Conference , vol. 2015 -July, pp. 703–716, 2015, doi: 10.1109/ACC.2015.7170817

    work page doi:10.1109/acc.2015.7170817 2015

  9. [9]

    Multi -objective optimization of demand response in a datacenter with lithium-ion battery storage,

    A. Mamun, I. Narayanan, D. Wang, A. Sivasubramaniam, and H. K. Fathy, “Multi -objective optimization of demand response in a datacenter with lithium-ion battery storage,” J. Energy Storage , vol. 7, pp. 258–269, Aug. 2016, doi: 10.1016/j.est.2016.08.002

    work page doi:10.1016/j.est.2016.08.002 2016

  10. [10]

    Physics -based simulation of the impact of demand response on lead - acid emergency power availability in a datacenter,

    A. Mamun, D. Wang, I. Narayanan, A. Sivasubramaniam, and H. K. Fathy, “Physics -based simulation of the impact of demand response on lead - acid emergency power availability in a datacenter,” J. Power Sources, vol. 275, pp. 516 –524, Feb. 2015, doi: 10.1016/j.jpowsour.2014.11.025

    work page doi:10.1016/j.jpowsour.2014.11.025 2015

  11. [11]

    Critical review and functional safety of a battery management system for large-scale lithium- ion battery pack technologies,

    K. W. See et al., “Critical review and functional safety of a battery management system for large-scale lithium- ion battery pack technologies,” Int. J. Coal Sci. Technol., vol. 9, no. 1, p. 36, Dec. 2022, doi: 10.1007/s40789-022- 00494-0

    work page doi:10.1007/s40789-022- 2022

  12. [12]

    A LiFePO4 battery pack capacity estimation approach considering in - parallel cell safety in electric vehicles,

    L. Wang, Y . Cheng, and X. Zhao, “A LiFePO4 battery pack capacity estimation approach considering in - parallel cell safety in electric vehicles,” Appl. Energy , vol. 142, pp. 293 –302, Mar. 2015, doi: 10.1016/j.apenergy.2014.12.081

    work page doi:10.1016/j.apenergy.2014.12.081 2015

  13. [13]

    Flyback Converter Balancing Technique for Lithium Based Batteries,

    A. Farzan Moghaddam and A. Van den Bossche, “Flyback Converter Balancing Technique for Lithium Based Batteries,” in International Conference on Modern Circuits and Systems Technologies (MOCAST), IEEE, May 2019. doi: 10.1109/MOCAST.2019.8741893

    work page doi:10.1109/mocast.2019.8741893 2019

  14. [14]

    Comparison of Active Battery Balancing Systems,

    M. Caspar, T. Eiler, and S. Hohmann, “Comparison of Active Battery Balancing Systems,” in 2014 IEEE Vehicle Power and Propulsion Conference (VPPC) , IEEE, Oct. 2014, pp. 1 –8. doi: 10.1109/VPPC.2014.7007027

    work page doi:10.1109/vppc.2014.7007027 2014

  15. [15]

    Investigation of active cell balancing performance for series connected lithium -ion cells in electric vehicle applications,

    U. Krishnamoorthy, G. S. Satheesh Kumar, S. Barua, and H. H. Fayek, “Investigation of active cell balancing performance for series connected lithium -ion cells in electric vehicle applications,” IET Power Electronics , 2023, doi: 10.1049/pel2.12575

    work page doi:10.1049/pel2.12575 2023

  16. [16]

    Analysis and control of charge and temperature imbalance within a lithium -ion battery pack,

    D. J. Docimo and H. K. Fathy, “Analysis and control of charge and temperature imbalance within a lithium -ion battery pack,” IEEE Transactions on Control Systems Technology, vol. 27, no. 4, pp. 1622 –1635, 2018, doi: 10.1109/TCST.2018.2819966

    work page doi:10.1109/tcst.2018.2819966 2018

  17. [17]

    Optimal Multiobjective Charging for Lithium-Ion Battery Packs: A Hierarchical Control Approach,

    Q. Ouyang, J. Chen, J. Zheng, and H. Fang, “Optimal Multiobjective Charging for Lithium-Ion Battery Packs: A Hierarchical Control Approach,” IEEE Trans. Industr. Inform., vol. 14, no. 9, pp. 4243 –4253, Sep. 2018, doi: 10.1109/TII.2018.2825245

    work page doi:10.1109/tii.2018.2825245 2018

  18. [18]

    A new perspective on battery cell balancing: Thermal balancing and relative temperature control,

    Y . Li and Y . Han, “A new perspective on battery cell balancing: Thermal balancing and relative temperature control,” in IEEE Energy Conversion Congress and Exposition, Institute of Electrical and Electronics Engineers Inc., 2016. doi: 10.1109/ECCE.2016.7854719

    work page doi:10.1109/ecce.2016.7854719 2016

  19. [19]

    Intelligent control battery equalization for series connected lithium -ion battery strings,

    Y . S. Lee and M. W. Cheng, “Intelligent control battery equalization for series connected lithium -ion battery strings,” IEEE Transactions on Industrial Electronics , vol. 52, no. 5, pp. 1297 –1307, Oct. 2005, doi: 10.1109/TIE.2005.855673

    work page doi:10.1109/tie.2005.855673 2005

  20. [20]

    State- of-Charge (SOC)-Balancing Control of a Battery Energy Storage System Based on a Cascade PWM Converter,

    L. Maharjan, S. Inoue, H. Akagi, and J. Asakura, “State- of-Charge (SOC)-Balancing Control of a Battery Energy Storage System Based on a Cascade PWM Converter,” IEEE Trans. Power Electron., vol. 24, no. 6, pp. 1628 – 1636, 2009, doi: 10.1109/TPEL.2009.2014868

    work page doi:10.1109/tpel.2009.2014868 2009

  21. [21]

    Multivariable State Feedback Control as a Foundation for Lithium -Ion Battery Pack Charge and Capacity Balancing,

    D. J. Docimo and H. K. Fathy, “Multivariable State Feedback Control as a Foundation for Lithium -Ion Battery Pack Charge and Capacity Balancing,” J. Electrochem. Soc., vol. 164Docimo, no. 2, pp. A61–A70, 2017, doi: 10.1149/2.0151702jes

    work page doi:10.1149/2.0151702jes 2017

  22. [22]

    V oltage balancing converter network for series -connected battery stack,

    T. H. Phung, J. C. Crebier, and Y . Lembeye, “V oltage balancing converter network for series -connected battery stack,” in IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, IEEE, Oct. 2012, pp. 3007–3013. doi: 10.1109/IECON.2012.6389418

    work page doi:10.1109/iecon.2012.6389418 2012

  23. [23]

    Influence of V oltage 9 Balancing on the Temperature Distribution of a Li -Ion Battery Module,

    U. Iraola, I. Aizpuru, L. Gorrotxategi, J. M. C. Segade, A. E. Larrazabal, and I. Gil, “Influence of V oltage 9 Balancing on the Temperature Distribution of a Li -Ion Battery Module,” IEEE Transactions on Energy Conversion, vol. 30, no. 2, pp. 507 –514, Jun. 2015, doi: 10.1109/TEC.2014.2366375

    work page doi:10.1109/tec.2014.2366375 2015

  24. [24]

    Circularly Polarized High Gain Monopole Antenna for 5G Applications,

    S. S M, S. Reddy, and Y . K. Kishore, “Modeling and Simulation Analysis of Cell V oltage Balancing Techniques for Lithium-Ion EV Battery,” in 2024 Third International Conference on Distributed Computing and Electrical Circuits and Electronics (ICDCECE) , IEEE, Apr. 2024, pp. 1 –6. doi: 10.1109/ICDCECE60827.2024.10548602

    work page doi:10.1109/icdcece60827.2024.10548602 2024

  25. [25]

    Temperature Control to Reduce Capacity Mismatch in Parallel -Connected Lithium Ion Cells,

    M. Garg, T. R. Tanim, C. D. Rahn, H. Bryngelsson, and N. Legnedahl, “Temperature Control to Reduce Capacity Mismatch in Parallel -Connected Lithium Ion Cells,” in ASME Dynamic Systems and Control Conference , Park City, Utah, Oct. 2019. [Online]. Available: http://asmedigitalcollection.asme.org/DSCC/proceeding s- pdf/DSCC2019/59148/V001T08A006/6455312/v00...

    work page 2019

  26. [26]

    An Investigation into the Viability of Cell -Level Temperature Control in Lithium-Ion Battery Packs,

    P. T. Abadie and D. J. Docimo, “An Investigation into the Viability of Cell -Level Temperature Control in Lithium-Ion Battery Packs,” ASME Letters in Dynamic Systems and Control , vol. 5, no. 1, Jan. 2025, doi: 10.1115/1.4066514

    work page doi:10.1115/1.4066514 2025

  27. [27]

    Optimal control and state estimation of lithium-ion batteries using reformulated models,

    B. Suthar et al., “Optimal control and state estimation of lithium-ion batteries using reformulated models,” in 2013 American Control Conference , IEEE, Jun. 2013, pp. 5350–5355. doi: 10.1109/ACC.2013.6580673

    work page doi:10.1109/acc.2013.6580673 2013

  28. [28]

    Comparative Analysis of Control Observer-Based Methods for State Estimation of Lithium-Ion Batteries in Practical Scenarios,

    M. Saeed et al. , “Comparative Analysis of Control Observer-Based Methods for State Estimation of Lithium-Ion Batteries in Practical Scenarios,” IEEE/ASME Transactions on Mechatronics , 2024, doi: 10.1109/TMECH.2024.3459644

    work page doi:10.1109/tmech.2024.3459644 2024

  29. [29]

    Electrode - Level State Estimation in Lithium -Ion Batteries via Kalman Decomposition,

    D. Zhang, L. D. Couto, and S. J. Moura, “Electrode - Level State Estimation in Lithium -Ion Batteries via Kalman Decomposition,” IEEE Control Syst. Lett. , vol. 5, no. 5, pp. 1657 –1662, Nov. 2021, doi: 10.1109/LCSYS.2020.3042751

    work page doi:10.1109/lcsys.2020.3042751 2021

  30. [30]

    Controllability, observability, and integrated state estimation and control of networked battery systems,

    L. Y . Wang, F. Lin, and W. Chen, “Controllability, observability, and integrated state estimation and control of networked battery systems,” IEEE Transactions on Control Systems Technology , vol. 26, no. 5, pp. 1699 – 1710, Sep. 2018, doi: 10.1109/TCST.2017.2727440

    work page doi:10.1109/tcst.2017.2727440 2018

  31. [32]

    Observability Analysis and State Estimation of Lithium -Ion Batteries in the Presence of Sensor Biases,

    S. Zhao, S. R. Duncan, and D. A. Howey, “Observability Analysis and State Estimation of Lithium -Ion Batteries in the Presence of Sensor Biases,” IEEE Transactions on Control Systems Technology, vol. 25, no. 1, pp. 326–333, Jan. 2017, doi: 10.1109/TCST.2016.2542115

    work page doi:10.1109/tcst.2016.2542115 2017

  32. [33]

    Observability analysis of a Li -ion cell equivalent circuit model based on interval arithmetic,

    S. Fasolato and D. M. Raimondo, “Observability analysis of a Li -ion cell equivalent circuit model based on interval arithmetic,” in 2022 IEEE Vehicle Power and Propulsion Conference (VPPC), IEEE, Nov. 2022. doi: 10.1109/VPPC55846.2022.10003466

    work page doi:10.1109/vppc55846.2022.10003466 2022

  33. [34]

    Observability and Estimability for State and Parameter Estimation in Li -Ion Battery Systems Under Different Parameter Configurations,

    R. Zheng, K. H. Kwak, J. -H. Han, and Y . Kim, “Observability and Estimability for State and Parameter Estimation in Li -Ion Battery Systems Under Different Parameter Configurations,” in 2025 IEEE/AIAA Transportation Electrification Conference and Electric Aircraft Technologies Symposium (ITEC+EATS), IEEE, Jun. 2025, pp. 1 –6. doi: 10.1109/ITEC63604.2025.11098039

    work page doi:10.1109/itec63604.2025.11098039 2025

  34. [35]

    Sensitivity -based interval PDE observer for battery SOC estimation,

    H. E. Perez and S. J. Moura, “Sensitivity -based interval PDE observer for battery SOC estimation,” in 2015 American Control Conference (ACC) , IEEE, Jul. 2015, pp. 323–328. doi: 10.1109/ACC.2015.7170756

    work page doi:10.1109/acc.2015.7170756 2015

  35. [36]

    Comparative Nonlinear Observability Analysis of Spatial Discretization Schemes for Lithium-Ion Battery Models,

    J. N. E. Lucero and S. Onori, “Comparative Nonlinear Observability Analysis of Spatial Discretization Schemes for Lithium-Ion Battery Models,” in American Control Conference, Denver: IEEE, Jul. 2025, pp. 2805– 2810

    work page 2025

  36. [37]

    Linearized Versus Nonlinear Observability Analysis for Lithium -Ion Battery Dynamics: Why Respecting the Nonlinearities Is Key for Proper Observer Design,

    A. Allam and S. Onori, “Linearized Versus Nonlinear Observability Analysis for Lithium -Ion Battery Dynamics: Why Respecting the Nonlinearities Is Key for Proper Observer Design,” IEEE Access, vol. 9, pp. 163431–163440, 2021, doi: 10.1109/ACCESS.2021.3130631

    work page doi:10.1109/access.2021.3130631 2021

  37. [38]

    Equalization of Lithium-Ion Battery Pack Based on Fuzzy Logic Control in Electric Vehicle,

    Y . Ma, P. Duan, Y . Sun, and H. Chen, “Equalization of Lithium-Ion Battery Pack Based on Fuzzy Logic Control in Electric Vehicle,” IEEE Transactions on Industrial Electronics, vol. 65, no. 8, pp. 6762 –6771, Aug. 2018, doi: 10.1109/TIE.2018.2795578

    work page doi:10.1109/tie.2018.2795578 2018

  38. [39]

    Cell Balancing Control for Lithium -Ion Battery Packs: A Hierarchical Optimal Approach,

    Q. Ouyang, W. Han, C. Zou, G. Xu, and Z. Wang, “Cell Balancing Control for Lithium -Ion Battery Packs: A Hierarchical Optimal Approach,” IEEE Trans. Industr. Inform., vol. 16, no. 8, pp. 5065 –5075, Aug. 2020, doi: 10.1109/TII.2019.2950818

    work page doi:10.1109/tii.2019.2950818 2020

  39. [40]

    Development and Application of an Active Balancing System for Lithium -Ion Cells,

    A. Ziegler, D. Oeser, T. Hein, and A. Ackva, “Development and Application of an Active Balancing System for Lithium -Ion Cells,” in IEEE Vehicle Power and Propulsion Conference (VPPC), 2019

    work page 2019

  40. [41]

    Control -Oriented Modeling of Lithium -Ion Batteries,

    B. J. C. Riemann, J. Li, K. Adewuyi, R. G. Landers, and J. Park, “Control -Oriented Modeling of Lithium -Ion Batteries,” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, vol. 143, no. 2, Feb. 2021, doi: 10.1115/1.4048355

    work page doi:10.1115/1.4048355 2021

  41. [42]

    Electrochemical Control of Lithium -Ion Batteries,

    K. A. Smith, “Electrochemical Control of Lithium -Ion Batteries,” IEEE Control Syst., vol. 30, no. 2, pp. 18–25, 2010, doi: 10.1109/MCS.2010.935882

    work page doi:10.1109/mcs.2010.935882 2010

  42. [43]

    Control oriented 1D electrochemical model of lithium ion battery,

    K. A. Smith, C. D. Rahn, and C. Y . Wang, “Control oriented 1D electrochemical model of lithium ion battery,” Energy Convers. Manag. , vol. 48, no. 9, pp. 2565–2578, Sep. 2007, doi: 10.1016/j.enconman.2007.03.015

    work page doi:10.1016/j.enconman.2007.03.015 2007

  43. [44]

    A Joint Analysis and Estimation Effort for Cell -to-Cell Variations in Lithium -Ion Battery Packs,

    P. T. Abadie, T. R. Jahan, and D. J. Docimo, “A Joint Analysis and Estimation Effort for Cell -to-Cell Variations in Lithium -Ion Battery Packs,” IEEE 10 Transactions on Control Systems Technology , vol. 33, no. 2, pp. 760 –774, Mar. 2025, doi: 10.1109/TCST.2024.3516364

    work page doi:10.1109/tcst.2024.3516364 2025

  44. [45]

    Nonlinear Controllability and Observability,

    R. Hermann and A. J. Krener, “Nonlinear Controllability and Observability,” IEEE Trans. Automat. Contr. , vol. AC-22, no. 5, pp. 728–740, Oct. 1977

    work page 1977

  45. [46]

    Physical controllability of complex networks,

    L. Z. Wang, Y . Z. Chen, W. X. Wang, and Y . C. Lai, “Physical controllability of complex networks,” Sci. Rep., vol. 7, Jan. 2017, doi: 10.1038/srep40198

    work page doi:10.1038/srep40198 2017

  46. [47]

    L. N. Trefethen and D. Bau, Numerical Linear Algebra. SIAM, 1997

    work page 1997

  47. [48]

    Experimental degradation study of a commercial lithium -ion battery,

    L. Wildfeuer, A. Karger, D. Aygül, N. Wassiliadis, A. Jossen, and M. Lienkamp, “Experimental degradation study of a commercial lithium -ion battery,” J. Power Sources, vol. 560, Mar. 2023, doi: 10.1016/j.jpowsour.2022.232498

    work page doi:10.1016/j.jpowsour.2022.232498 2023

  48. [49]

    Analytical derivation and analysis of parameter sensitivity for battery electrochemical dynamics,

    Q. Lai, S. Jangra, H. J. Ahn, G. Kim, W. T. Joe, and X. Lin, “Analytical derivation and analysis of parameter sensitivity for battery electrochemical dynamics,” J. Power Sources , vol. 472, p. 228338, Oct. 2020, doi: 10.1016/j.jpowsour.2020.228338

    work page doi:10.1016/j.jpowsour.2020.228338 2020

  49. [50]

    In: 2020 American Control Conference (ACC), pp

    Q. Lai, H. J. Ahn, G. Kim, W. T. Joe, and X. Lin, “Optimization of Current Excitation for Identification of Battery Electrochemical Parameters based on Analytic Sensitivity Expression,” in 2020 American Control Conference (ACC), IEEE, Jul. 2020, pp. 346 –351. doi: 10.23919/ACC45564.2020.9147575

    work page doi:10.23919/acc45564.2020.9147575 2020

  50. [51]

    Comprehensive Modeling of Temperature -Dependent Degradation Mechanisms in Lithium Iron Phosphate Batteries,

    M. Schimpe, M. E. von Kuepach, M. Naumann, H. C. Hesse, K. Smith, and A. Jossen, “Comprehensive Modeling of Temperature -Dependent Degradation Mechanisms in Lithium Iron Phosphate Batteries,” J. Electrochem. Soc. , vol. 165, no. 2, pp. A181 –A193, 2018, doi: 10.1149/2.1181714jes

    work page doi:10.1149/2.1181714jes 2018

  51. [52]

    On the use of electrochemical impedance spectroscopy to characterize and model the aging phenomena of lithium-ion batteries: a critical review,

    P. Iurilli, C. Brivio, and V . Wood, “On the use of electrochemical impedance spectroscopy to characterize and model the aging phenomena of lithium-ion batteries: a critical review,” Sep. 01, 2021, Elsevier B.V . doi: 10.1016/j.jpowsour.2021.229860

    work page doi:10.1016/j.jpowsour.2021.229860 2021

  52. [53]

    A Review of Second -Life Lithium -Ion Batteries for Stationary Energy Storage Applications,

    X. Hu et al. , “A Review of Second -Life Lithium -Ion Batteries for Stationary Energy Storage Applications,” Jun. 01, 2022, Institute of Electrical and Electronics Engineers Inc. doi: 10.1109/JPROC.2022.3175614

    work page doi:10.1109/jproc.2022.3175614 2022

  53. [54]

    Fair Market Value of Used Capacity Assets: Forecasts for Repurposed Electric Vehicle Batteries,

    A. Bach, S. Onori, S. Reichelstein, and J. Zhuang, “Fair Market Value of Used Capacity Assets: Forecasts for Repurposed Electric Vehicle Batteries,” The Accounting Review, pp. 1 –23, Dec. 2025, doi: 10.2308/TAR -2025- 0024

    work page doi:10.2308/tar 2025