Skip to main content
Log in

Recursive partial stabilization: Backstepping and generalized strict feedback form

  • Regular Papers
  • Control Theory
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

Recursive design and partial stabilization are considered where the method of recursive design is combined with the concept of partial stabilization. A generalized strict feedback form for partial stabilization is presented followed by stabilization process.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. D. Sontag, Mathematical Control Theory, Springer, 1998.

    MATH  Google Scholar 

  2. S. B. Townley, “An example of a globally stabilizing adaptive controller with a generically destabilizing parameter estimate,” IEEE Trans. on Automatic Control, vol. 44, no. 11, pp. 2238–2241, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Krstić, I. Kanellakopoulos, and P. V. Kokotović, Nonlinear and Adaptive Control Design, Wiley, 1995.

    Google Scholar 

  4. A. S. Andreyev, “Investigation of partial asymptotic stability and instability based on the limiting equations,” J. Appl. Maths. Mechs. vol. 51, no. 2, pp. 196–201, 1987.

    Article  MathSciNet  Google Scholar 

  5. C. Risito, “Sulla stabilita parziale,” Ann. Math. Pura Appl. vol. 4, no. 84, pp. 279–292, 1970.

    MathSciNet  Google Scholar 

  6. V. V. Rumyantsev, “On the stability of motion with respect to the part of the variables,” Vestnik Moscow Univ.Ser.Mat.Mech.Fiz.Astron.Khim., vol. 4, pp, 9–16, 1957.

    Google Scholar 

  7. V. V. Rumyantsev and A. S. Oziraner, The Stability and Stabilization of Motion with Respect to Some of the Variables, Nauka, 1987.

    Google Scholar 

  8. V. I. Vorotnikov, “Partial stability and control: the state-of-the-art and development prospects,” Automation and Remote Control, vol. 66, no. 4, pp. 511–561, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  9. V. Chellaboina and W. M. Haddad, “A unification between partial stability and stability theory for time-varying systems,” IEEE Trans. on Control Systems, vol. 22, no. 6, pp. 66–75, 2003.

    Article  Google Scholar 

  10. A. N. Michel and Y. Sun, “Partial stability of general dynamical systems under arbitrary initial z-Perturbations,” Proc. of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, 2002.

    Google Scholar 

  11. Y. Sun, A. P. Molchanov, and A. N. Michel, “Partial stability of dynamical systems,” Proc. of the 15th Int. Symp. on Mathematical Theory of Networks and Systems, University of Notre Dame, 2002.

    Google Scholar 

  12. V. I. Vorotnikov, Partial Stability and Control, Birkhäuser, 1998.

    MATH  Google Scholar 

  13. C. Corduneanu, “Sur la stabilité partielle,” Rev. Roumaine Math. Pures Appl., vol. 9, pp. 229–236, 1964.

    MathSciNet  MATH  Google Scholar 

  14. A. S. Andreyev, “An investigation of partial asymptotic stability,” J. Appl. Maths. Mechs., vol. 55, no. 4, pp. 429–435, 1991.

    Article  Google Scholar 

  15. A. S. Oziraner, “On asymptotic stability and instability relative to a part of variables,” J. Appl. Maths. Mechs, vol. 37, pp. 659–665, 1973.

    Article  MathSciNet  Google Scholar 

  16. A. Isidori, Nonlinear Control Systems, Springer, 1995.

    MATH  Google Scholar 

  17. G. R. Rokni Lamooki, Adaptive and Non-Linear Control, Bifurcation, Computation and Partial Stabilisation, Ph.D. Thesis, University of Exeter, UK, 2003.

    Google Scholar 

  18. Y. Hu, Y. Jing, and P. Cui, “RBF NN-bases backstepping control for strict feedback block nonlinear systems and its applications,” in Y. J. Wang and C. Guo (Eds.), LNCS, vol. 3174, pp. 129–137, 2004.

  19. J. W. C. Robinson and U. Nilsson, “Design of a nonlinear autopilot for velocity and attitude control using block backstepping,” Proc. of AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California, 2005.

    Google Scholar 

  20. Y. Chang and C. C. Cheng, “Block backstepping control of multi input nonlinear systems with mismatched perturbations for asymptotic stability,” International Journal of Control, vol. 83, no. 10, pp. 2028–2039, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  21. Y. Chang, “Block backstepping control of MIMO Systems,” IEEE Trans. on Automatic Control, vol. 56, no. 5, pp. 1191–1197, 2011.

    Article  Google Scholar 

  22. I. G. Malkin, Theory of Stability of Motion, 2nd Ed., Izdat. Nauka, Moscow, 1966.

    MATH  Google Scholar 

  23. H. K. Khalil, Nonlinear Systems and Control, Prentice-Hall, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gholam Rreza Rokni Lamooki.

Additional information

Recommended by Editorial Board member Kyong Su Yi under the direction of Editor Zengqi Sun.

The author thanks S. B. Townley and H. M. Osinga for their valuable comments, and anonymous referees whose comments and suggestions substantially improved this paper.

Gholam Rreza Rokni Lamooki received his BSC in Engineering from Ferdowsi University, an MSC in Mathematics from Kharazmi University, and a PhD in Mathematics, from University of Exeter in 1993, 1997, and 2003, respectively. He is interested in dynamical systems, control theory and their applications.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lamooki, G.R.R. Recursive partial stabilization: Backstepping and generalized strict feedback form. Int. J. Control Autom. Syst. 11, 250–257 (2013). https://doi.org/10.1007/s12555-011-0172-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-011-0172-9

Keywords

Navigation