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Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics

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Abstract

The output feedback stabilization is considered for a class of nonlinear time-delay systems with inverse dynamics in this paper. An appropriate state observer is constructed for the unmeasurable system states in order to realize the control objective. By adopting the backstepping and Lyapunov-Krasovskii functional methods, a systematic design procedure for a memoryless output feedback control law is presented. It is shown that the designed controller can make the closed-loop system globally asymptotically stable while keeping all signals bounded. An illustrative example is discussed to show the effectiveness of the proposed control strategy.

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References

  1. V. Kolmanovskii, A. Myshkis. Introduction to the Theory and Applications of Functional Differential Equations, Dordrecht, Holland: Kluwer Academic, 1999.

    MATH  Google Scholar 

  2. J. K. Hale, S. M. V. Lunel. Introduction to Functional Differential Equation, Berlin, Germany: Springer, pp. 58–133, 1993.

    Google Scholar 

  3. P. Pepe, Z. P. Jiang. A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems. Systems and Control Letters, vol. 55, no. 12, pp. 1006–1014, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  4. Q. Zhu, D. G. Hu. Converse Lyapunov theorem of inputtostate stability for time-delay systems. Acta Automatica Sinica, vol. 36, no. 8, pp. 1131–1136, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  5. C. C. Hua, X. P. Guan, P. Shi. Robust backstepping control for a class of time delayed systems. IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 894–899, 2005.

    Article  MathSciNet  Google Scholar 

  6. C. C. Hua, G. Feng, X. P. Guan. Robust controller design of a class of nonlinear time delay systems via backstepping method. Automatica, vol. 44, no. 2, pp. 567–573, 2008.

    Article  MathSciNet  Google Scholar 

  7. S. S. Ge, F. Hong, T. H. Lee. Adaptive neural network control of nonlinear systems with unknown time delays. IEEE Transactions on Automatic Control, vol. 48, no. 11, pp. 2004–2010, 2003.

    Article  MathSciNet  Google Scholar 

  8. D. W. C. Ho, J. M. Li, Y. G. Niu. Adaptive neural control for a class of nonlinearly parametric time-delay systems. IEEE Transactions on Neural Networks, vol. 16, no. 3, pp. 625–635, 2005.

    Article  Google Scholar 

  9. X. F. Zhang, Z. L. Zhao. Output feedback stabilization of nonlinear systems with delays in the input. Applied Mathematics and Computation, vol. 167, no. 2, pp. 1026–1040, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. J. Liu, S. S. Ge, J. F. Zhang. Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays. International Journal of Control, vol. 81, no. 8, pp. 1210–1220, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Guan. Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays. International Journal of Systems Science, vol. 43, no. 4, pp. 682–690, 2012.

    Article  MathSciNet  Google Scholar 

  12. L. Liu, X. J. Xie. Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay. Automatica, vol. 47, no. 12, pp. 2772–2779, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. M. Li, C. E. Ren, S. C. Tong. Adaptive fuzzy backstepping output feedback control of nonlinear uncertain timedelay systems based on high-gain filters. Nonlinear Dynamics, vol. 69, no. 3, pp. 781–792, 2012.

    Article  Google Scholar 

  14. S. C. Tong, N. Sheng. Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay. International Journal of Automation and Computing, vol. 7, no. 2, pp. 236–246, 2010.

    Article  Google Scholar 

  15. B. Z. Du, J. Lam, Z. Shu. Stabilization for state/input delay systems via static and integral output feedback. Automatica, vol. 46, no. 12, pp. 2000–2007, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  16. C. L. Liu, S. C. Tong, Y. M. Li, Y. Q. Xia. Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign. International Journal of Automation and Computing, vol.8, no. 1, pp. 14–22, 2011.

    Article  Google Scholar 

  17. C. C. Hua, X. P. Guan, P. Shi. Robust output feedback tracking control for time-delay nonlinear systems using neural network. IEEE Transactions on Neural Networks, vol. 18, no. 2, pp. 495–505, 2007.

    Article  Google Scholar 

  18. H. K. Khalil. Nonlinear Systems, 3rd ed, New Jersey, USA: Prentice Hall, pp. 144–323, 2002.

    MATH  Google Scholar 

  19. N. Duan, X. Yu, X. J. Xie. Output feedback control using small-gain conditions for stochastic nonlinear systems with SiISS inverse dynamics. International Journal of Control, vol. 81, no. 1, pp. 47–56, 2011.

    Article  MathSciNet  Google Scholar 

  20. W. Lin, C. J. Qian. Adaptive control of nonlinearly parameterized systems: A nonsmooth feedback framework. IEEE Transactions on Automatic Control, vol. 47, no. 5, pp. 757–774, 2002.

    Article  MathSciNet  Google Scholar 

  21. J. Liu, X. Z. Liu, W. C. Xie. Input-to-state stability of impulsive and switching hybrid systems with time-delay. Automatica, vol. 47, no. 5, pp. 899–908, 2011.

    Article  MathSciNet  MATH  Google Scholar 

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Author notes

  1. Yu-Qiang Wu

    Present address: Institute of Automation, Qufu Normal University, Qufu, 273165, China

Authors and Affiliations

  1. Institute of Automation, Qufu Normal University, Qufu, 273165, China

    Zhong-Cai Zhang

Authors
  1. Zhong-Cai Zhang
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  2. Yu-Qiang Wu
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Additional information

This work was supported by National Natural Science Foundation of China (No. 60974127) and Natural Science Foundation of Shandong Province of China (No. ZR2011FM033).

Zhong-Cai Zhang graduated from Ludong University, China in 2010. He is currently a master student at the Institute of Automation, Qufu Normal University, China.

His research interests include variable structure control and nonlinear system control.

Yu-Qiang Wu graduated from Qufu Normal University, China in 1985. He received the M. Sc. degree from Qufu Normal University in 1988 and the Ph.D. degree from Southeast University, China in 1994.

He is currently a professor in the Institute of Automation, Qufu Normal University. His research interests include variable structure control, switching control, nonlinear system control, and process control.

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Zhang, ZC., Wu, YQ. Globally asymptotic stabilization for nonlinear time-delay systems with ISS inverse dynamics. Int. J. Autom. Comput. 9, 634–640 (2012). https://doi.org/10.1007/s11633-012-0689-2

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  • DOI: https://doi.org/10.1007/s11633-012-0689-2

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