Skip to main content
SpringerLink
Log in

Semi-global stabilization via homogeneous output feedback for a class of nonlinear time-delay systems

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

Abstract

The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous domination approach, a homogeneous observer and an output feedback controller with a scaling gain are designed. Then the scaling gain is adjusted such that the closed-loop system is semi-global asymptotically stable. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.

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. Gong Q and Lin W, A note on global output regulation of nonlinear systems in the output feedback form, IEEE Trans. Automatic Control, 2003, 48(6): 1049–1054.

    Article  MathSciNet  Google Scholar 

  2. Qian C J and Lin W, Output feedback control of a class of nonlinear systems: A nonseparation principle paradign, IEEE Trans. Automatic Control, 2002, 47(10): 1710–1715.

    Article  MathSciNet  Google Scholar 

  3. Qian C J, A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems, Proceedings of American Control Conference, 2005, 4708–4715.

    Google Scholar 

  4. Gong Q and Qian C J, Global practical tracting of a class of nonlinear systems by output feedback, Automatica, 2007, 43(1): 184–189.

    Article  MathSciNet  MATH  Google Scholar 

  5. Qian C J and Lin W, A continuous feedback approach to global strong stabilization of nonlinear systems, IEEE Trans. Automatic Control, 2001, 46(7): 1061–1079.

    Article  MathSciNet  MATH  Google Scholar 

  6. Qian C J, Semi-global stabilization of a class of uncertain nonlinear systems by linear output feedback, IEEE Transactions on Circuits and Systems II: Express Briefs, 2005, 52(4): 218–222.

    Article  Google Scholar 

  7. Zhai J Y, Zha W T, and Fei S M, Semi-global finite-time output feedback stabilization for a class of large-scale uncertain nonlinear systems, Commun. Nonlinear Sci. Numer. Simulat., 2013, 18(11): 3181–3189.

    Article  MathSciNet  MATH  Google Scholar 

  8. Jia R T and Qian C J, Semi-global finite-time stabilization of a class of nonlinear systems by output feedback, 49th IEEE Conference on Decision and Control, 2010, 2169–2174.

    Chapter  Google Scholar 

  9. Yu Y and Zhong Y, Semi-global robust output tracking for non-linear uncertain systems in strictfeedback form, IET Control Theory and Applications, 2012, 6(5): 751–759.

    Article  MathSciNet  Google Scholar 

  10. Zhai J Y and Du H B, Semi-global output feedback stabilization for a class of nonlinear systems using homogeneous domination approach, ISA Transactions, 2013, 52(2): 231–241.

    Article  Google Scholar 

  11. Tian W S, Du H B, and Qian C J, A semi-global finite-time convergent observer for a class of nonlinear systems with bounded trajectories, Nonlinear Analysis: Real World Applications, 2012, 13(4): 1827–1836.

    Article  MathSciNet  MATH  Google Scholar 

  12. Jia R T, Qian C J, and Zhai J Y, Semi-global stabilisation of uncertain non-linear systems by homogeneous output feedback controllers, IET Control Theory and Applications, 2012, 6(1): 165–172.

    Article  MathSciNet  Google Scholar 

  13. Chai L and Qian C J, Global stabilization via homogeneous output feedback for a class of uncertain nonlinear systems subject to time-delays, Transactions of the Institute of Measurement and Control, 2014, 36(4): 478–486.

    Article  Google Scholar 

  14. Chai L, Global stabilization for a class of nonlinear time-delay systems using linear output feedback, Journal of Southeast University (English Edition), 2013, 29(3): 264–269.

    MathSciNet  MATH  Google Scholar 

  15. Zhai J Y and Zha W T, Global adaptive output feedback control for a class of nonlinear time-delay systems, ISA Transactions, 2014, 53(1): 2–9.

    Article  Google Scholar 

  16. Ye X D, Adaptive stabilization of time-delay feedforward nonlinear systems, Automatica, 2011, 47(5): 950–955.

    Article  MathSciNet  MATH  Google Scholar 

  17. Wu M, He Y, She J H, et al., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 2004, 40(3): 1435–1439.

    Article  MathSciNet  MATH  Google Scholar 

  18. Yakoubi K and Chitour Y, Linear systems subject to input saturation and time-delay: Global asymptotic stabilization, IEEE Trans. Automatic Control, 2007, 52(5): 874–879.

    Article  MathSciNet  MATH  Google Scholar 

  19. Gu K Q, Kharitonov V L, and Chen J, Stability of Time-Delay Systems, Birkhäuser, Boston, 2003.

    Book  MATH  Google Scholar 

  20. Hua C C, Liu P X, and Guan X P, Backstepping control for nonlinear systems with time delays and applications to chemical reactor systems, IEEE Transactions on Industrial Electronics, 2009, 56(9): 3723–3732.

    Article  Google Scholar 

  21. Sun Z Y and Liu Y G, State-feedback stabilization control design for a class of time-delay highorder nonlinear systems, Proceedings of the 30th Chinese Control Conference, 2011, 476–480.

    Google Scholar 

  22. Li J, Qian C J, and Frye M T, A dual observer design for global output feedback stabilization of nonlinear systems with low-order and high-order nonlinearities, International Journal of Robust and Nonlinear Control, 2009, 19(15): 1697–1720.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing, 210096, China

    Pan Wang, Lin Chai & Shumin Fei

  2. School of Automation, Southeast University, Nanjing, 210096, China

    Pan Wang, Lin Chai & Shumin Fei

Authors
  1. Pan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shumin Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pan Wang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61374038, 61473079, and 61374060.

This paper was recommended for publication by Editor SUN Jian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, P., Chai, L. & Fei, S. Semi-global stabilization via homogeneous output feedback for a class of nonlinear time-delay systems. J Syst Sci Complex 29, 1538–1552 (2016). https://doi.org/10.1007/s11424-016-5037-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-016-5037-0

Keywords

Search

Navigation