Passivity of discrete-time port-Hamiltonian systems for power-electronic applications

Authors

Kenneth Marín-Silva, Walter Gil-González, Alejandro Garcés-Ruiz

Abstract

This paper investigates the preservation of passivity in the discrete-time modeling of a class of port-Hamiltonian systems arising in power-electronic applications. We analyze the most commonly used discretization schemes and derive sufficient conditions under which each method preserves passivity. The results show, through passivity indicators and simulation studies, that the modified passive output obtained from the proposed framework preserves passivity, whereas the classical discrete-time passive output may violate it. For cases in which passivity is not inherently guaranteed, a systematic procedure to determine an admissible discretization step is provided. It is shown that the Exact, Backward Euler, Midpoint, and RK4 methods preserve passivity independently of the step size, while Forward Euler exhibits a maximum admissible step beyond which passivity is lost. Mathematical models are presented for applications in power electronics. However, the reader does not require specialized expertise in this area to reproduce results. The findings confirm that preserving passivity—rather than symplecticity—is the key requirement for the intended applications and that a rigorous analytical framework is necessary to ensure this property in discrete time.

Keywords

ac/dc converters, dc/dc converters, discretization of ordinary differential equations, passivity, port-hamiltonian systems, power and energy applications, power electronics

Citation

• Journal: Applied Mathematical Modelling
• Year: 2026
• Volume: 157
• Issue:
• Pages: 116993
• Publisher: Elsevier BV
• DOI: 10.1016/j.apm.2026.116993

BibTeX

@article{Mar_n_Silva_2026,
  title={{Passivity of discrete-time port-Hamiltonian systems for power-electronic applications}},
  volume={157},
  ISSN={0307-904X},
  DOI={10.1016/j.apm.2026.116993},
  journal={Applied Mathematical Modelling},
  publisher={Elsevier BV},
  author={Marín-Silva, Kenneth and Gil-González, Walter and Garcés-Ruiz, Alejandro},
  year={2026},
  pages={116993}
}

Download the bib file

References

• Van der Schaft, (2014)
• Gil-González W, Garces A, Escobar A (2019) Passivity-based control and stability analysis for hydro-turbine governing systems. Applied Mathematical Modelling 68:471–486. https://doi.org/10.1016/j.apm.2018.11.04 – 10.1016/j.apm.2018.11.045
• Tõnso M, Kaparin V, Belikov J (2023) Port-Hamiltonian framework in power systems domain: A survey. Energy Reports 10:2918–2930. https://doi.org/10.1016/j.egyr.2023.09.07 – 10.1016/j.egyr.2023.09.077
• Gil-González W, Montoya OD, Garces A (2020) Standard passivity-based control for multi-hydro-turbine governing systems with surge tank. Applied Mathematical Modelling 79:1–17. https://doi.org/10.1016/j.apm.2019.11.01 – 10.1016/j.apm.2019.11.010
• Sanz-Serna JM (1992) Symplectic integrators for Hamiltonian problems: an overview. Acta Numerica 1:243–286. https://doi.org/10.1017/s096249290000228 – 10.1017/s0962492900002282
• Garcés-Ruiz A, Riffo S, González-Castaño C, Restrepo C (2024) Model Predictive Control With Stability Guarantee for Second-Order DC/DC Converters. IEEE Trans Ind Electron 71(5):5157–5165. https://doi.org/10.1109/tie.2023.328370 – 10.1109/tie.2023.3283706
• Mattioni A, Wu Y, Le Gorrec Y (2020) Infinite dimensional model of a double flexible-link manipulator: The Port-Hamiltonian approach. Applied Mathematical Modelling 83:59–75. https://doi.org/10.1016/j.apm.2020.02.00 – 10.1016/j.apm.2020.02.008
• Xu B, Wang F, Chen D, Zhang H (2016) Hamiltonian modeling of multi-hydro-turbine governing systems with sharing common penstock and dynamic analyses under shock load. Energy Conversion and Management 108:478–487. https://doi.org/10.1016/j.enconman.2015.11.03 – 10.1016/j.enconman.2015.11.032
• Gernandt H, Severino B, Zhang X, Mehrmann V, Strunz K (2025) Port-Hamiltonian Modeling and Control of Electric Vehicle Charging Stations. IEEE Trans Transp Electrific 11(1):2897–2907. https://doi.org/10.1109/tte.2024.342954 – 10.1109/tte.2024.3429545
• Kotyczka P, Lefèvre L (2019) Discrete-time port-Hamiltonian systems: A definition based on symplectic integration. Systems & Control Letters 133:104530. https://doi.org/10.1016/j.sysconle.2019.10453 – 10.1016/j.sysconle.2019.104530
• Macchelli A (2023) Control Design for a Class of Discrete-Time Port-Hamiltonian Systems. IEEE Trans Automat Contr 68(12):8224–8231. https://doi.org/10.1109/tac.2023.329218 – 10.1109/tac.2023.3292180
• Moreschini, Discrete time PID passivity-Based control of a class of bilinear systems including power converters. (2025)
• Macchelli A (2024) A Discrete-Time Formulation of Nonlinear Distributed-Parameter Port-Hamiltonian Systems. IEEE Control Syst Lett 8:802–807. https://doi.org/10.1109/lcsys.2024.340476 – 10.1109/lcsys.2024.3404769
• Chan C-Y (2008) Simplified parallel-damped passivity-based controllers for dc–dc power converters. Automatica 44(11):2977–2980. https://doi.org/10.1016/j.automatica.2008.05.00 – 10.1016/j.automatica.2008.05.005
• Gil-González, Adaptive control for second-order DC-DC converters: PBC approach. (2021)
• Reddy, Constant power load in DC microgrid system: a passivity based control of two input integrated DC-DC converter. e-Prime-Adv. Electr. Eng. Electron. Energy (2025)
• Son YI, Kim IH (2012) Complementary PID Controller to Passivity-Based Nonlinear Control of Boost Converters With Inductor Resistance. IEEE Trans Contr Syst Technol 20(3):826–834. https://doi.org/10.1109/tcst.2011.213409 – 10.1109/tcst.2011.2134099
• Zhao F, Wang X, Zhu T (2023) Low-Frequency Passivity-Based Analysis and Damping of Power-Synchronization Controlled Grid-Forming Inverter. IEEE J Emerg Sel Topics Power Electron 11(2):1542–1554. https://doi.org/10.1109/jestpe.2022.321884 – 10.1109/jestpe.2022.3218845
• Mehrmann V, Van Dooren P (2020) Optimal robustness of passive discrete-time systems. IMA Journal of Mathematical Control and Information 37(4):1248–1269. https://doi.org/10.1093/imamci/dnaa01 – 10.1093/imamci/dnaa013
• Vuillemin E, Martin J-P, Machmoum M, Pierfederici S, Meibody-Tabar F (2026) Novel singularity-free IDA-PBC design method for stable interconnection of boost converters. Mathematics and Computers in Simulation 241:257–270. https://doi.org/10.1016/j.matcom.2025.10.00 – 10.1016/j.matcom.2025.10.006
• Zheng F, Yin H, Han Z, Guo B-Z (2026) Exponential stability preserving of two spatially discretized port-Hamiltonian systems. Journal of Differential Equations 453:113865. https://doi.org/10.1016/j.jde.2025.11386 – 10.1016/j.jde.2025.113865
• Sanz-Serna, (1994)
• Cordoni FG, Di Persio L, Muradore R (2022) Discrete stochastic port-Hamiltonian systems. Automatica 137:110122. https://doi.org/10.1016/j.automatica.2021.11012 – 10.1016/j.automatica.2021.110122
• Moreschini A, Mattioni M, Monaco S, Normand-Cyrot D (2021) Stabilization of Discrete Port-Hamiltonian Dynamics via Interconnection and Damping Assignment. IEEE Control Syst Lett 5(1):103–108. https://doi.org/10.1109/lcsys.2020.300070 – 10.1109/lcsys.2020.3000705
• Haine G, Matignon D, Monteghetti F (2022) Structure-preserving discretization of Maxwell’s equations as a port-Hamiltonian system. IFAC-PapersOnLine 55(30):424–429. https://doi.org/10.1016/j.ifacol.2022.11.09 – 10.1016/j.ifacol.2022.11.090
• Ponce, A port-Hamiltonian framework for the modeling and FEM discretization of hyperelastic systems. Appl. Math. Model. (2025)
• Warsewa A, Böhm M, Sawodny O, Tarín C (2021) A port-Hamiltonian approach to modeling the structural dynamics of complex systems. Applied Mathematical Modelling 89:1528–1546. https://doi.org/10.1016/j.apm.2020.07.03 – 10.1016/j.apm.2020.07.038
• Brugnoli A, Alazard D, Pommier-Budinger V, Matignon D (2019) Port-Hamiltonian formulation and symplectic discretization of plate models Part I: Mindlin model for thick plates. Applied Mathematical Modelling 75:940–960. https://doi.org/10.1016/j.apm.2019.04.03 – 10.1016/j.apm.2019.04.035
• Fränken D, Ochs K (2001) Synthesis and Design of Passive Runge-Kutta Methods. AEU - International Journal of Electronics and Communications 55(6):417–425. https://doi.org/10.1078/1434-8411-5410006 – 10.1078/1434-8411-54100062
• Fränken D, Ochs K (2003) Passive Runge–Kutta Methods—Properties, Parametric Representation, and Order Conditions. BIT Numerical Mathematics 43(2):339–361. https://doi.org/10.1023/a:102603982000 – 10.1023/a:1026039820006
• Ortega, Stabilization of port-controlled hamiltonian systems via energy balancing. (1999)
• Lin W, Byrnes CI (1994) KYP lemma, state feedback and dynamic output feedback in discrete-time bilinear systems. Systems & Control Letters 23(2):127–136. https://doi.org/10.1016/0167-6911(94)90042- – 10.1016/0167-6911(94)90042-6
• Kazmierkowski, Control in Power Electronics: selected problems. (2002)
• Moreschini A, He W, Ortega R, Lu Y, Li T (2026) Globally stable discrete time PID Passivity-based Control of power converters: Simulation and experimental results. Automatica 189:112976. https://doi.org/10.1016/j.automatica.2026.11297 – 10.1016/j.automatica.2026.112976
• Hairer, (1993)
• Estrada L, Vázquez N, Tafoya PI, Gonzalez JEE, Ortega J, Vazquez J (2023) Practical considerations for HIL simulations of power converters using different numerical methods. JART 21(6):899–911. https://doi.org/10.22201/icat.24486736e.2023.21.6.181 – 10.22201/icat.24486736e.2023.21.6.1816
• Yushkova M, Sanchez A, de Castro A (2021) Strategies for choosing an appropriate numerical method for FPGA-based HIL. International Journal of Electrical Power & Energy Systems 132:107186. https://doi.org/10.1016/j.ijepes.2021.10718 – 10.1016/j.ijepes.2021.107186
• Revathy, Powering the future: a comprehensive review on DC-DC converters and their vital role in electric vehicle technology. (2024)
• Sharma S, Gupta S, Zuhaib M, Bhuria V, Malik H, Almutairi A, Afthanorhan A, Hossaini MA (2024) A Comprehensive Review on STATCOM: Paradigm of Modeling, Control, Stability, Optimal Location, Integration, Application, and Installation. IEEE Access 12:2701–2729. https://doi.org/10.1109/access.2023.334521 – 10.1109/access.2023.3345216
• Hussen M, Rajaram T (2025) A Comprehensive Review of Voltage Source Converters-Based FACTS Controllers in Hybrid Microgrids. IEEE Access 13:62961–62999. https://doi.org/10.1109/access.2025.355796 – 10.1109/access.2025.3557961
• Sira-Ramírez, (2006)
• Oyuela-Ocampo J-C, Garcés-Ruiz A, Gil-González W (2026) Generalized model-predictive control for supercapacitor and superconducting magnetic energy storage systems. Renewable Energy Focus 57:100795. https://doi.org/10.1016/j.ref.2025.10079 – 10.1016/j.ref.2025.100795