On Strong Stability and Stabilizability of Linear Systems of Neutral Type

  • Rabah Rabah
  • Grigory M. Sklyar
  • Alexandr V. Rezounenko
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 38)


For linear stationary systems, the infinite dimensional framework allows one to distinguish different notions of stability: weak, strong or exponential. The purpose of this chapler is to investigate the problem of strong stability, i.e. asymptotic non-exponential stability for linear systems of neutral type in order to use this characterization in the study of the stabilizability problem for this type of systems. An important tool in this investigation is the Riesz basis property of generalized eigenspaces of the neutral system, because that the generalized eigenvectors do not form, in general, a Riesz basis. This allows one to describe more precisely asymptotic non-exponential stability of neutral systems. For a particular case, conditions of strong stabilizability of neutral type systems are given with a feedback law without derivative of the delayed state.


Functional Differential Equation Riesz Basis Strong Stability Infinitesimal Generator Neutral System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Rabah Rabah
    • 1
  • Grigory M. Sklyar
    • 2
  • Alexandr V. Rezounenko
    • 3
  1. 1.IRCCyN UMR 6597, 1 rue de la NoëNantes Cedex 3France
  2. 2.Institute of Mathematics, University of SzczecinSzczecinPoland
  3. 3.Department of Mechanics and MathematicsKharkov UniversityKharkovUkraine

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