Stability of Operators and Operator Semigroups

This book is about stability of linear dynamical systems, discrete and continuous. More precisely, we discuss convergence to zero of strongly continuous semigroups of operators and of powers of a bounded linear operator, both with respect to different topologies. The discrete and the continuous case...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Eisner, Tanja (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Basel : Springer Basel : Imprint: Birkhäuser, 2010.
Édition:1st ed. 2010.
Collection:Operator Theory: Advances and Applications, 209
Sujets:
Operator theory.
Dynamical systems.
System theory.
Control theory.
Operator Theory.
Dynamical Systems.
Systems Theory, Control .
Accès en ligne:Texto Completo
Table des matières:
  • Introduction
  • Chapter I. Functional analytic tools
  • 1. Structure of compact semigroups
  • 2. Mean ergodicity
  • 3. Tools from semigroup theory
  • Chapter II. Stability of linear operators
  • 1. Power boundedness
  • 2. Strong stability
  • 3. Weak stability
  • 4. Almost weak stability
  • 5. Abstract examples
  • 6. Stability via Lyapunov equation
  • Chapter III. Stability of C0-semigroups
  • 1. Boundedness
  • 2. Uniform exponential stability
  • 3. Strong stability
  • 4. Weak stability
  • 5. Almost weak stability
  • 6. Abstract examples
  • 7. Stability via Lyapunov equation
  • Chapter IV. Discrete vs. continuous
  • 1. Embedding operators into C0-semigroups
  • 2. Cogenerators
  • Bibliography.

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