Skip to main content
SpringerLink
Log in

Stabilization of linear control systems in Hilbert space with nonlinear feedback

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

This paper considers the problem of stabilization of linear control systems in Hilbert space with nonlinear feedback. Extensions of known results in the linear feedback case to the nonlinear one are given.

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. Ball J.,Strong continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Soc.,63 (1977), 370–373.

    Article  MATH  Google Scholar 

  2. Ball J., Slemro, M.,Feedback stabilization of distributed semilinear control systems, Appl. Math. Optim.,5 (1979), 169–179.

    Article  MATH  MathSciNet  Google Scholar 

  3. Benchimol C. D.,A note on weak stabilizability of contraction semigroups, SIAM J. Control Optim.,16 (1978), 373–379.

    Article  MATH  MathSciNet  Google Scholar 

  4. Berrahmoune L.,Stabilization of beams with nonlinear feedback, SIAM J. Control Optim.,41 (2002), 1166–1193.

    Article  MATH  MathSciNet  Google Scholar 

  5. Brezis H.,Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, (Mathematics Studies 5, North-Holland), 1973.

  6. Conrad F., Pierre M.,Stabilization of second order evolution equations by unbounded npnlinear feedback, Ann. Inst. Henri Poincaré,11(5) (1994), 485–515.

    MathSciNet  Google Scholar 

  7. Dafermos C., Slemrod M.,Asymptotic behaviour of nonlinear contraction semigroups, J. Functional Analysis,13 (1973), 97–106.

    Article  MATH  MathSciNet  Google Scholar 

  8. Datko R.,Uniform asymptotic stability of evolutionary processes in Banach spaces, SIAM J. Math. Anal.,3 (1972), 428–445.

    Article  MATH  MathSciNet  Google Scholar 

  9. Foguel S.R.,Powers of a contraction in Hilbert spaces, Pacific J. Math.,13 (1963), 551–562.

    MATH  MathSciNet  Google Scholar 

  10. Gutman P.O., Hagander P.,A new design of constrained controllers for linear systems.IEEE Trans, Automat. Control,30 (1985), 22–25

    Article  MATH  MathSciNet  Google Scholar 

  11. Levan N.,The stabilization problem: A Hilbert space operator decomposition approach.IEEE Trans, Circuits and systems CAS,25(9) (1978), 721–727.

    Article  MATH  MathSciNet  Google Scholar 

  12. Sz.-Nagy B., Foias C.,Analyse harmonique des opérateurs de l’espace de Hilbert (Masson et Cie, Akadémai Kiadó, Budapest, French edition, Masson et Cie), 1967.

  13. Pazy A.,A class of semilinear equations of evolution, Israel J. Math.,20 (1975), 23–36.

    Article  MATH  MathSciNet  Google Scholar 

  14. Pazy A.,Semigroups of linear operators and applications to partial differential equations, (Springer Verlag), 1983.

  15. Seidman T.I, Li H.,A note on stabilization with sturating feedback, Discrete and continuous dynamical systems,7 (2001), 319–328.

    Article  MATH  MathSciNet  Google Scholar 

  16. Slemrod M.,Anote on complete controllability and stabilizability for linear control systems in Hilbert space, SIAM J. Control,12 (1974), 500–508.

    Article  MathSciNet  Google Scholar 

  17. Slemrod M.,Feedback stabilization of a linear control system in Hilbert space with a priori bounded control, Math. Control Signals Systems,2 (1989), 265–285.

    Article  MATH  MathSciNet  Google Scholar 

  18. Web G. F.,Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Funct. Anal.,10 (1972), 191–203.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Ecole Normale Supérieure de Rabat, BP 5118, Rabat, Morocco

    Larbi Berrahmoune

Authors
  1. Larbi Berrahmoune
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Larbi Berrahmoune.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berrahmoune, L. Stabilization of linear control systems in Hilbert space with nonlinear feedback. Rend. Circ. Mat. Palermo 54, 273–290 (2005). https://doi.org/10.1007/BF02874641

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02874641

AMS Subject Classification

Search

Navigation