Skip to main content
SpringerLink
Log in

Further stability results for a generalization of delayed feedback control

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we consider the stabilization of unstable periodic orbits for one-dimensional and discrete time chaotic systems. Various control schemes for this problem are available and we consider a recent generalization of delayed control scheme. We prove that if a certain condition, which depends only on the period number, is satisfied then the stabilization is always possible. We will also present some simulation results.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Chen, G., Dong, X.: From Chaos to Order: Methodologies, Perspectives and Applications. World Scientific, Singapore (1999)

    Google Scholar 

  2. Fradkov, A.L., Evans, R.J.: Control of chaos: methods and applications in engineering. Annu. Rev. Control 29, 33–56 (2005)

    Article  Google Scholar 

  3. Devaney, R.L.: Chaotic Dynamical Systems. Addison-Wesley, Redwood City (1987)

    Google Scholar 

  4. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  5. Pyragas, K.: Continuous control of chaos by self controlling feedback. Phys. Lett. A 170, 421–428 (1992)

    Article  Google Scholar 

  6. Ushio, T.: Limitation of delayed feedback control in nonlinear discrete time systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 43, 815–816 (1996)

    Article  Google Scholar 

  7. Morgül, Ö.: On the stability of delayed feedback controllers. Phys. Lett. A 314, 278–285 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Morgül, Ö.: A new generalization of delayed feedback control. Int. J. Bifurc. Chaos. 19, 365–377 (2009)

    Article  MATH  Google Scholar 

  9. Morgül, Ö.: On the stability of delayed feedback controllers for discrete time systems. Phys. Lett. A 335, 31–42 (2005)

    Article  MATH  Google Scholar 

  10. Morgül, Ö.: On the stabilization of periodic orbits for discrete time chaotic systems. Phys. Lett. A 335, 127–138 (2005)

    Article  MATH  Google Scholar 

  11. Ushio, T., Yamamoto, S.: Prediction based control of chaos. Phys. Lett. A 264, 30–35 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Vieira, d.S.M., Lichtenberg, A.J.: Controlling chaos using nonlinear feedback with delay. Phys. Rev. E 54, 1200–1207 (1996)

    Article  Google Scholar 

  13. Morgül, Ö.: Stabilization of unstable periodic orbits for discrete time chaotic systems by using periodic feedback. Int. J. Bifurc. Chaos 16, 311–323 (2006)

    Article  MATH  Google Scholar 

  14. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Upper Saddle River (2002)

    MATH  Google Scholar 

  15. Fuh, C.C., Tung, P.C.: Controlling chaos using differential geometric method. Phys. Rev. Lett. 75, 2952–2955 (1995)

    Article  Google Scholar 

  16. Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1966)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Electrical Eng., Bilkent University, 06800, Bilkent Ankara, Turkey

    Ömer Morgül

Authors
  1. Ömer Morgül
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ömer Morgül.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morgül, Ö. Further stability results for a generalization of delayed feedback control. Nonlinear Dyn 70, 1255–1262 (2012). https://doi.org/10.1007/s11071-012-0530-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-012-0530-z

Keywords

Search

Navigation