Acta Mathematica Hungarica

, Volume 103, Issue 4, pp 321–348 | Cite as

Observability of coupled systems

  • Michel Mehrenberger


By applying the theory of semigroups, we generalize an earlier result of Komornik and Loreti [5] on the observability of compactly perturbed systems. As an application, we answer a question of the same authors concerning the observability of weakly coupled linear distributed systems.

nonharmonic analysis wave equation semigroups Riesz basis observability Petrovsky system 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. Alabau, Observabilité frontière de systèmes faiblement couplésC.R. Acad. Sci. Paris Sér. I, 333 (2001), 645–650.zbMATHMathSciNetGoogle Scholar
  2. [2]
    I. Gohberg, S. Goldberg and M. A. KaashoekClasses of Linear Operators, Birkhäuser-Verlag (1990).Google Scholar
  3. [3]
    A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaireJ. Math. Pures Appl., 68 (1989), 457–465.zbMATHMathSciNetGoogle Scholar
  4. [4]
    V. Komornik and P. Loreti, Ingham type theorems for vector-valued functions and observability of coupled linear systemsSIAM J. Control Optim., 37 (1998), 461–485.MathSciNetCrossRefGoogle Scholar
  5. [5]
    V. Komornik and P. Loreti, Observability of compactly perturbed systemsJ. Math. Anal. Appl., 243 (2000), 409–428.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    V. Komornik and P. Loreti, Boundary observability of compactly perturbed systems, in: Proceedings of the Conference on Control of Distributed Parameter Systems (Graz, 2001), to appear.Google Scholar
  7. [7]
    A. PazySemigroups of Linear Operators and Applications to Partial Differential Equations, Springer (1983).Google Scholar
  8. [8]
    J. L. LionsContrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Vol. 1, Rech. Math. Appl. 8, Masson (Paris, 1988).Google Scholar
  9. [9]
    J. L. Lions, Exact controllability, stabilization and perturbations for distributed systemsSIAM Review, 30 (1988), 1–68.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publisher/Akadémiai Kiadó 2004

Authors and Affiliations

  • Michel Mehrenberger
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur et CNRSStrasbourg CedexFrance

Personalised recommendations