Skip to main content

Stabilisation d'une classe de systèmes distribués hyperboliques

  • Hyperbolic Control Systems
  • Conference paper
  • First Online:
  • 2007 Accesses

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 111))

Résumé

On se propose de stabiliser un système hyperbolique général par retour statique de sortie. La stabilisation exponentielle ne pouvant avoir lieu, on montre qu'il est possible d'obtenir une stabilisation asymptotique. On donne des applications où cette dernière est assurée par un choix convenable de capteurs et d'actionneurs.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Références

  • 1 A.V. BALAKRISHNAN. Strong stabilizability and the steady state Riccati equation. App.Math. Optim.7, p.335–345 (1981).

    Google Scholar 

  • 2 C. BARDOS, G. CHEN. Control and stabilization for the wave equation part III: domain with moving boundary Siam J.Contr.Optim, vol 19, p.123–138. 1981.

    Google Scholar 

  • 3 C.D. BENCHIMOL. A note on weak stabilizability of contraction semigroups. Siam J. Control and optim.vol 16,no3,p.373–379, 1978.

    Google Scholar 

  • 4 G. CHEN. A note on the boundary stabilization of the wave equation. Siam J.Contr. Optim. Vol.19,pp 106–113, 1981.

    Google Scholar 

  • 5 G. CHEN. Control and stabilization for the wave equation in a bounded domain, part.II, Siam J.Contr.Optim, Vol.19, p.114–122, 1981.

    Google Scholar 

  • 6 R.F. CURTAIN, A.J. PRITCHARD. Infinite dimensional linear systems theory. Lecture notes in control and information sciences. vol.8. Springer Verlag, 1978.

    Google Scholar 

  • 7 N.DUNFORD, J.T.SCHWARTZ. Linear operators, vol 3, interscience, 1971.

    Google Scholar 

  • 8 A. EL JAI, A.J. PRITCHARD. Capteurs et actionneurs dans l'analyse des systèmes distribués. Masson, Paris, 1986.

    Google Scholar 

  • 9 J.S. GIBSON. A note on stabilization of infinite dimensional linear oscillators by compact linear feedback. Siam J.Control and optim. vol.18, p.311–316, 1980.

    Google Scholar 

  • 10 T.KATO. Perturbation theory for linear operators, 2nd ed., Springer Verlag, 1980.

    Google Scholar 

  • 11 I. LASIECKA, R. TRIGGIANI. A cosine operator approach to modelling L2(O,T,L2(Γ))-boundary input hyperbolic equations.App.Math. Optim.7, p.35–93 (1981).

    Google Scholar 

  • 12 I. LASIECKA, R. TRIGGIANI. Dirichlet boundary stabilization of the wave equation with damping feedback of finite range.J.Math An. and App. 97 p. 112–1130, 1983.

    Google Scholar 

  • 13 J.L. LIONS. J. Von Neuman lecture, Boston, SIAM Meeting, July 1986.

    Google Scholar 

  • 14 T. NAMBU. Feedback stabilization for distributed parameter system of parabolic type. J.Diff. Eq. 33, p.167–188 (1979).

    Google Scholar 

  • 15 A.PAZY. Semigroups of linear operators and applications to partial differential equations. App. Math. Sciences 44, Springer Verlag 1984.

    Google Scholar 

  • 16 D. RUSSEL. Decay rates for weakly damped systems in Hilbert space obtained via control-theoretic methods J.Diff. Eq. 19 (1975), p.344–370.

    Google Scholar 

  • 17 D. RUSSEL. Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions. Siam Review, vol 20, p. 639–739, 1978.

    Google Scholar 

  • 18 M. SLEMROD. A note on complete controllability and stabilizability of linear control systems in Hilbert Space. Siam J. Control Vol.12, p.500–508, 1974.

    Google Scholar 

  • 19 M. SLEMROD. Stabilization of boundary control systems. J.Diff. Eq. 22, 402–415 (1976).

    Google Scholar 

  • 20 SUN SCHUNHUA. Boundary stabilization of hyperbolic systems with no dissipative conditions. Siam J. Control Optim. Vol 20, no6 p. 862–883, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. Bensoussan J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Berrahmoune, L. (1988). Stabilisation d'une classe de systèmes distribués hyperboliques. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042238

Download citation

  • DOI: https://doi.org/10.1007/BFb0042238

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19237-4

  • Online ISBN: 978-3-540-39161-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics