Skip to main content
SpringerLink
Log in

Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances. In case there is no perturbation, the exponential convergence of the observer was confirmed. When external disturbances appear in the system, a separation principle is established, and the authors show that the closed loop system is exponentially practical stable. By choosing a suitable Lyapunov-Krasovskii functional, the authors derive new sufficient conditions to guarantee the exponential stability of the systems. Finally, a physical model is performed to prove the efficiency and applicability of the suggested approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rajamani R, Observers for Lipschitz nonlinear systems, IEEE Trans. Automat. Control, 1998, 43(3): 397–401.

    Article  MathSciNet  MATH  Google Scholar 

  2. Hu G, Observers for one-sided lipschitz non-linear systems, IMA Journal of Mathematical Control and Information, 2006, 23(4): 395–401.

    Article  MathSciNet  MATH  Google Scholar 

  3. Abbaszadeh M and Marquez H J, Nonlinear observer design for one-sided Lipschitz systems, Proc. American Control Conf., Baltimore, USA, 2010, 5284–5289.

  4. Zhang W, Su H, Liang Y, et al., Nonlinear observer design for one-sided Lipschitz systems: A linear matrix inequality approach, IET Contr. Theory Appl., 2012, 6(9): 1297–1303.

    Article  Google Scholar 

  5. Zhang W, Liang Y, Su H S, et al., LMI-based observer design for one-sided Lipschitz nonlinear systems, Proc. 30th Chinese Control Conference, Yantai, China, 2011, 256–260.

  6. El-Haiek B, EL Aiss H, Hmamed A, et al., Robust observer design of one-sided Lipschitz nonlinear systems, Annual American Control Conference, USA, June 27–29, 2018, 5250–5255.

  7. Huang J, Yu L, and Shi M J, Adaptive observer design for quasi-one-sided lipschitz nonlinear systems, Proceedings of 2017 Chinese Intelligent Systems Conference, 2017, 13–22.

  8. He S, Lyu W, and Liu F, Robust H∞ sliding mode controller design of a class of time-delayed discrete conic-type nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(2): 885–892.

    Article  Google Scholar 

  9. Lu G and Ho D, Robust H∞ observer for a class of nonlinear discrete systems with time delay and parameter uncertainties, IEEE Proceedings Control Theory Application, 2004, 151: 439–444.

    Article  Google Scholar 

  10. Zhang W, Su H, Su S, et al., Nonlinear H∞ observer design for one-sided Lipschitz systems, Neurocomputing, 2014, 145: 505–511.

    Article  Google Scholar 

  11. Dastaviz A and Binazadeh T, Simultaneous stabilization for a collection of uncertain time-delay systems using sliding-mode output feedback control, Int. J. Control, 2020, 93(9): 2135–2144.

    Article  MathSciNet  MATH  Google Scholar 

  12. Echi N and Ghanmi B, Global rational stabilization of a class of nonlinear time-delay systems, Arch. Control Sci., 2019, 29: 259–278.

    MathSciNet  MATH  Google Scholar 

  13. Ekramian M, Ataei M, and Talebi S, Stability of nonlinear time-delay systems satisfying a quadratic constraint, Trans. Inst. Meas. Control, 2018, 40(3): 712–718.

    Article  Google Scholar 

  14. Yang Y, Lin C, Chen B, et al., Reduced-order observer design for a class of generalized Lipschitz nonlinear systems with time-varying delay, Appl. Math. Comput., 2018, 337: 267–280.

    MathSciNet  MATH  Google Scholar 

  15. Zhu Q and Hu G, Stability analysis for uncertain nonlinear time-daly systems with quasi-onesided Lipschitz condition, Acta Automat. Sinca, 2009, 35: 1006–1009.

    Google Scholar 

  16. Zhang Z and Xu S, Observer design for uncertain nonlinear systems with unmodeled dynamics, Automatica, 2015, 51: 80–84.

    Article  MathSciNet  MATH  Google Scholar 

  17. Echi N, Observer design and practical stability of nonlinear systems under unknown time-delay, Asian Journal of Control, 2021, 23(2): 685–696.

    Article  MathSciNet  Google Scholar 

  18. Echi N and Benabdallah A, Obsever besed control for strong practical stabilization of a class of uncertain time delay systems, Kybernetika, 2020, 55(6): 1016–1033.

    MATH  Google Scholar 

  19. Dong Y, Liu W, and Liang S, Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties, International Journal of Robust and Nonlinear Control, 2017, 27(11): 1974–1998.

    Article  MathSciNet  MATH  Google Scholar 

  20. Asadinia M A and Binazadeh T, Finite-time stabilization of descriptor time-delay systems with one-sided Lipschitz nonlinearities: Application to partial element equivalent circuit, Circuits, Systems, and Signal Processing, 2019, 38(12): 5467–5487.

    Article  Google Scholar 

  21. Gholami H and Binazadeh T, Observer-based H∞ finite-time controller for time-delay nonlinear one-sided Lipschitz systems with exogenous disturbances, J. Vib. Control, 2018, https://doi.org/10.1177/1077546318802422.

  22. Ahmad S, Majeed R, Hong K S, et al., Observer design for one-sided Lipschitz nonlinear systems subject to measurement delays, Mathematical Problems in Engineering, 2015, Article ID 879492, 13 pages, https://doi.org/10.1155/2015/879492.

  23. Nguyen M C and Trinh H, Reduced-order observer design for one-sided Lipschitz time-delay systems subject to unknown inputs, IET Control Theory Appl., 2016, 10(10): 1097–1105.

    Article  MathSciNet  Google Scholar 

  24. Ellouze I, Separation principle of time-varying systems including multiple delayed perturbations, Bulletin des Sciences Mathématiques, 2020, 161(1): 102869.

    Article  MathSciNet  MATH  Google Scholar 

  25. Ben Hamed B, Ellouze I, and Hammami M A, Practical uniform stability of nonlinear differential delay equation, Mediterranean Journal of Mathematics 2011, 8: 603–616.

    Article  MathSciNet  MATH  Google Scholar 

  26. Benabdallah A and Echi N, Global exponential stabilisation of a class of nonlinear time-delay systems, International Journal of Systems Science, 2016, 47: 3857–3863.

    Article  MathSciNet  MATH  Google Scholar 

  27. Echi N and Benabdallah A, Delay-dependent stabilization of a class of time-delay nonlinear systems: LMI approach, Advances in Difference Equations, 2017, 271, DOI: https://doi.org/10.1186/s13662-017-1335-7.

  28. Dong Y, Liu W, and Liang S, Reduced-order observer-based controller design for quasi-onesided Lipschitz nonlinear systems with time-delay, International Journal of Robust and Nonlinear Control, 2021, 31(3): 817–831.

    Article  MathSciNet  Google Scholar 

  29. Hu G D, Dong W, and Cong Y, Separation principle for quasi-one-sided Lipschitz nonlinear systems with time-delay, Int. J. Robust Nonlinear Control, 2020, 30(6): 2430–2442.

    Article  MathSciNet  MATH  Google Scholar 

  30. Liu P L, New results on stability analysis for time-varying delay systems with non-linear perturbations, ISA Transactions, 2013, 52: 318–325.

    Article  Google Scholar 

  31. Nie R, He S, Liu F, et al., Sliding mode controller design for conic-type nonlinear semi-Markovian jumping systems of time-delayed Chua’s circuit, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(4): 2467–2475.

    Article  Google Scholar 

  32. Cullum J, Ruehli A, and Zhang T, A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEEC models with retardation, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process, 2000, 47(4): 261–273.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Sciences of Gafsa, Department of Mathematics, Gafsa University, Zarroug Gafsa, Gafsa, 2112, Tunisia

    Echi Nadhem

  2. Faculty of Sciences of Sfax, Department of Mathematics, Sfax University, BP 1171, Sfax, 3000, Tunisia

    Akrouti Imen

Authors
  1. Akrouti Imen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Echi Nadhem
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Echi Nadhem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Imen, A., Nadhem, E. Global Practical Exponential Stabilization for One-Sided Lipschitz Systems with Time Delay. J Syst Sci Complex 35, 2029–2045 (2022). https://doi.org/10.1007/s11424-022-1061-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-022-1061-4

Keywords

Search

Navigation