Finite-time control design for a general class of switched uncertain nonlinear port-Hamiltonian systems

Authors

Yu-Han Liu, Zi-Ming Wang, Xudong Zhao, Xiaodi Li, Xianfu Zhang

Abstract

In this paper, utilizing energy-based multiple Lyapunov functions (EMLFs) analysis tools, we explore the issues concerning finite-time stabilization and finite-time H ∞ control for switched uncertain nonlinear port-Hamiltonian systems (SUNPHSs) under average dwell time (ADT) restrictions. To solve the impact of uncertain terms and relax the structure of EMLFs, the corresponding constraint conditions are adopted, based on which an improved ADT-based switching scheme is developed, and the sufficient criterion is put forward to ensure the finite-time stability (FTS) of SUNPHSs. Subsequently, a mode-dependent switching state feedback (MDSSF) controller is exploited to render the resulting closed-loop SUNPHSs FTS. Moreover, to attenuate disturbances, another MDSSF controller is presented to keep SUNPHSs possessing finite-time H ∞ performance under a new ADT-based switching scheme. Finally, three simulation examples, including a switched nonlinear circuit system, are provided to substantiate the feasibility of the derived finite-time control approaches.

Keywords

average dwell time, energy-based multiple lyapunov functions, finite-time stabilization, finite-time ℋ∞control, switched uncertain nonlinear port-hamiltonian systems

Citation

• Journal: Nonlinear Analysis: Hybrid Systems
• Year: 2026
• Volume: 62
• Issue:
• Pages: 101784
• Publisher: Elsevier BV
• DOI: 10.1016/j.nahs.2026.101784

BibTeX

@article{Liu_2026,
  title={{Finite-time control design for a general class of switched uncertain nonlinear port-Hamiltonian systems}},
  volume={62},
  ISSN={1751-570X},
  DOI={10.1016/j.nahs.2026.101784},
  journal={Nonlinear Analysis: Hybrid Systems},
  publisher={Elsevier BV},
  author={Liu, Yu-Han and Wang, Zi-Ming and Zhao, Xudong and Li, Xiaodi and Zhang, Xianfu},
  year={2026},
  pages={101784}
}

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References

• Zhu Y, Zheng WX (2020) Observer-Based Control for Cyber-Physical Systems With Periodic DoS Attacks via a Cyclic Switching Strategy. IEEE Trans Automat Contr 65(8):3714–3721. https://doi.org/10.1109/tac.2019.295321 – 10.1109/tac.2019.2953210
• Zhang, Output-based robust switching rule design for uncertain switched affine systems: application to DC-DC converters. IEEE Trans. Circuits Syst. II Express Briefs (2022)
• Liang Y, Zhang L, Wang X (2024) Antibump Switched LPV Control With Delayed Scheduling for Morphing Aircraft. IEEE Trans Aerosp Electron Syst 60(4):5010–5023. https://doi.org/10.1109/taes.2024.338417 – 10.1109/taes.2024.3384177
• Wu J-L (2009) Stabilizing controllers design for switched nonlinear systems in strict-feedback form. Automatica 45(4):1092–1096. https://doi.org/10.1016/j.automatica.2008.12.00 – 10.1016/j.automatica.2008.12.004
• Liu L, Yin Y, Wang J, Wu Q (2016) Stability analysis of discrete-time switched nonlinear systems via T–S fuzzy model approach. Neurocomputing 173:1967–1971. https://doi.org/10.1016/j.neucom.2015.08.00 – 10.1016/j.neucom.2015.08.007
• Long L, Wang F, Chen Z (2024) Global Event-Triggered Funnel Control of Switched Nonlinear Systems via Switching Multiple Lyapunov Functions. IEEE Trans Cybern 54(11):6731–6741. https://doi.org/10.1109/tcyb.2024.339939 – 10.1109/tcyb.2024.3399392
• Xu N, Wu Y, Zong G, Niu B, Zhao X (2026) Resilient Adaptive Secure Control for MIMO Switched CPSs Under Unknown Deception Attacks. IEEE Trans Green Commun Netw 10:1160–1170. https://doi.org/10.1109/tgcn.2025.361515 – 10.1109/tgcn.2025.3615157
• Zhao J, Hill DJ (2008) On stability, L2-gain and H∞ control for switched systems. Automatica 44(5):1220–1232. https://doi.org/10.1016/j.automatica.2007.10.01 – 10.1016/j.automatica.2007.10.011
• (1999) Basic problems in stability and design of switched systems. IEEE Control Syst 19(5):59–70. https://doi.org/10.1109/37.79344 – 10.1109/37.793443
• Branicky MS (1998) Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Automat Contr 43(4):475–482. https://doi.org/10.1109/9.66415 – 10.1109/9.664150
• Liberzon, (2003)
• Zhao X, Zhang L, Shi P, Liu M (2012) Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time. IEEE Trans Automat Contr 57(7):1809–1815. https://doi.org/10.1109/tac.2011.217862 – 10.1109/tac.2011.2178629
• Zhou W, Wang K, Zhu W (2024) Synchronization for discrete coupled fuzzy neural networks with uncertain information via observer-based impulsive control. MMC 4(1):17–31. https://doi.org/10.3934/mmc.202400 – 10.3934/mmc.2024003
• Tian Y, Sun Y, Liang M (2026) Stability of time-varying homogeneous systems with mixed delays and disturbances through novel nonlinear Halanay inequality. IEEE Trans Automat Contr :1–8. https://doi.org/10.1109/tac.2026.366512 – 10.1109/tac.2026.3665123
• Zhang W, Zong G, Niu B, Zhao X, Song G (2026) Adaptive neural self-triggered secure control for nonlinear networked PDE-ODE systems subject to unknown deception attacks. Information Sciences 745:123411. https://doi.org/10.1016/j.ins.2026.12341 – 10.1016/j.ins.2026.123411
• Xu N, Yue S, Zhao N, Niu B, Zhao X (2026) SMS‐Based Optimal Control of Completely Unknown Nonlinear Systems With Unknown Actuator Saturation. Adaptive Control & Signal. https://doi.org/10.1002/acs.7010 – 10.1002/acs.70109
• Khalil, (2002)
• Wang Y, Li C, Cheng D (2003) Generalized Hamiltonian realization of time-invariant nonlinear systems. Automatica 39(8):1437–1443. https://doi.org/10.1016/s0005-1098(03)00132- – 10.1016/s0005-1098(03)00132-8
• Xu S, Wang W, Chen S (2020) Energy‐based output regulation for stochastic port‐Hamiltonian systems. Intl J Robust & Nonlinear 31(5):1720–1734. https://doi.org/10.1002/rnc.537 – 10.1002/rnc.5377
• Toledo J, Wu Y, Ramírez H, Le Gorrec Y (2020) Observer-based boundary control of distributed port-Hamiltonian systems. Automatica 120:109130. https://doi.org/10.1016/j.automatica.2020.10913 – 10.1016/j.automatica.2020.109130
• Wu C, van der Schaft A, Chen J (2021) Stabilization of Port-Hamiltonian Systems Based on Shifted Passivity via Feedback. IEEE Trans Automat Contr 66(5):2219–2226. https://doi.org/10.1109/tac.2020.300515 – 10.1109/tac.2020.3005156
• Liu X, Liao X (2023) Fixed-Time Control for a Class of Nonlinear PH-DAE Systems. IEEE Trans Syst Man Cybern, Syst 53(8):5161–5173. https://doi.org/10.1109/tsmc.2023.325844 – 10.1109/tsmc.2023.3258447
• Zhi H, Liu Y, Yu H (2024) Adaptive exponential tracking control of port-Hamiltonian system via contraction and timed IDA-PBC method. Nonlinear Dyn 113(7):6879–6891. https://doi.org/10.1007/s11071-024-10473- – 10.1007/s11071-024-10473-6
• Wang Z-M, Wei A, Zhao X, Mu R, Zhang X (2020) Control design for switched port-controlled Hamiltonian systems with unstabilizable modes: An improved mode-dependent average dwell time scheme. Nonlinear Analysis: Hybrid Systems 38:100944. https://doi.org/10.1016/j.nahs.2020.10094 – 10.1016/j.nahs.2020.100944
• Zhu H, Hou X (2018) Passivity‐based parameterized adaptive disturbance attenuation controller design for switched polynomial nonlinear systems. Adaptive Control & Signal 32(9):1377–1392. https://doi.org/10.1002/acs.291 – 10.1002/acs.2919
• Zhu H, Hou X (2018) Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach. Intl J Robust & Nonlinear 28(16):4931–4950. https://doi.org/10.1002/rnc.429 – 10.1002/rnc.4296
• Zhang Q, Sun W, Qiao C (2022) Event-triggered stabilisation of switched nonlinear systems with actuator saturation: a Hamiltonian approach. International Journal of Systems Science 54(4):849–866. https://doi.org/10.1080/00207721.2022.214727 – 10.1080/00207721.2022.2147279
• control for switched non-linear systems with structural uncertainty by using robust passivity. Nonlinear Analysis: Hybrid Systems 40:101017. https://doi.org/10.1016/j.nahs.2021.10101 – 10.1016/j.nahs.2021.101017
• Lian J, Zhao J, Dimirovski GM (2010) Integral Sliding Mode Control for a Class of Uncertain Switched Nonlinear Systems. European Journal of Control 16(1):16–22. https://doi.org/10.3166/ejc.16.16-2 – 10.3166/ejc.16.16-22
• Wang Z-M, Zhao X, Li X, Zhang X, Mu R (2024) Energy-Based Control for Switched Uncertain Port-Controlled Hamiltonian Systems With Its Application to RLC Circuit Systems. IEEE Trans Syst Man Cybern, Syst 54(1):107–118. https://doi.org/10.1109/tsmc.2023.330601 – 10.1109/tsmc.2023.3306012
• Kamenkov, On stability of motion over a finite interval of time. J. Appl. Math. Mech. USSR (1953)
• Dong J, Ye Z, Zhang D (2024) Finite-Time Security Control of Networked Unmanned Marine Vehicle Systems Subject to DoS Attack. IEEE Trans Intell Veh 9(2):3464–3477. https://doi.org/10.1109/tiv.2024.335024 – 10.1109/tiv.2024.3350246
• Tong Y, Ren Z, Tong D, Fan Z, Feng X (2023) Combined finite‐time state feedback for high‐speed train systems with time‐varying delays and disturbances. Intl J Robust & Nonlinear 34(3):2184–2205. https://doi.org/10.1002/rnc.707 – 10.1002/rnc.7076
• He Y, Bai Y (2024) Finite-time stability and applications of positive switched linear delayed impulsive systems. MMC 4(2):178–194. https://doi.org/10.3934/mmc.202401 – 10.3934/mmc.2024016
• Amato F, Ariola M, Dorato P (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9):1459–1463. https://doi.org/10.1016/s0005-1098(01)00087- – 10.1016/s0005-1098(01)00087-5
• Li X, Lin X, Li S, Zou Y (2015) Finite-time stability of switched nonlinear systems with finite-time unstable subsystems. Journal of the Franklin Institute 352(3):1192–1214. https://doi.org/10.1016/j.jfranklin.2014.12.01 – 10.1016/j.jfranklin.2014.12.011
• Fei Z, Shi S, Ahn CK, Basin MV (2021) Finite-Time Control for Switched T–S Fuzzy Systems via a Dynamic Event-Triggered Mechanism. IEEE Trans Fuzzy Syst 29(12):3899–3909. https://doi.org/10.1109/tfuzz.2020.302929 – 10.1109/tfuzz.2020.3029292
• Chen H, Zong G, Shen M, Gao F (2025) Finite-Time Resilient Control of Networked Markov Switched Nonlinear Systems: A Relaxed Design. IEEE Trans Syst Man Cybern, Syst 55(4):2569–2579. https://doi.org/10.1109/tsmc.2025.352632 – 10.1109/tsmc.2025.3526321
• He S, Ai Q, Ren C, Dong J, Liu F (2019) Finite-Time Resilient Controller Design of a Class of Uncertain Nonlinear Systems With Time-Delays Under Asynchronous Switching. IEEE Trans Syst Man Cybern, Syst 49(2):281–286. https://doi.org/10.1109/tsmc.2018.279864 – 10.1109/tsmc.2018.2798644
• boundedness for nonlinear singular switched positive systems with D-perturbations. Nonlinear Analysis: Hybrid Systems 45:101208. https://doi.org/10.1016/j.nahs.2022.10120 – 10.1016/j.nahs.2022.101208
• Wang Z-M, Zhao X, Li X, Wei A (2023) Finite-time adaptive control for uncertain switched port-controlled Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulation 119:107129. https://doi.org/10.1016/j.cnsns.2023.10712 – 10.1016/j.cnsns.2023.107129
• Li C, Zhao J (2016) Robust passivity‐basedH∞control for uncertain switched nonlinear systems. Intl J Robust & Nonlinear 26(14):3186–3206. https://doi.org/10.1002/rnc.349 – 10.1002/rnc.3499
• Lv X, Niu Y, Song J (2021) Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach. Nonlinear Dyn 104(1):497–507. https://doi.org/10.1007/s11071-021-06292- – 10.1007/s11071-021-06292-8
• Wang Z-M, Wei A, Zong G, Zhao X, Li H (2020) Finite-time stabilization and H∞ control for a class of switched nonlinear port-controlled Hamiltonian systems subject to actuator saturation. Journal of the Franklin Institute 357(16):11807–11829. https://doi.org/10.1016/j.jfranklin.2019.11.05 – 10.1016/j.jfranklin.2019.11.055
• Bhat SP, Bernstein DS (2000) Finite-Time Stability of Continuous Autonomous Systems. SIAM J Control Optim 38(3):751–766. https://doi.org/10.1137/s036301299732135 – 10.1137/s0363012997321358
• control for switched linear systems via mode-dependent dynamic state-feedback. Nonlinear Analysis: Hybrid Systems 8:109–120. https://doi.org/10.1016/j.nahs.2012.12.00 – 10.1016/j.nahs.2012.12.001
• Zhao Z, Jie H, Tao M, Li H, Sun Q, Gao RX-K (2025) High-Frequency Impedance Modeling of Induction Motors Using Adaptive Multistage RLC Circuit and Neural Network-Based Stagewise Parameter Identification. IEEE Trans Ind Electron 72(4):3357–3369. https://doi.org/10.1109/tie.2024.345111 – 10.1109/tie.2024.3451119