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Spectral value sets of infinite-dimensional systems

  • E. Gallestey
  • D. Hinrichsen
  • A. J. Pritchard
Part of the Communications and Control Engineering book series (CCE)

Abstract

We assume that X, X, U, Y are complex or real separable Banach spaces, A with dense domain D(A) ⊂ X is a closed linear operator on X, D(A) ⊂ XX with continuous dense injections, B ∈ ℒ(U,X) and C ∈ ℒ (X,Y). Let K denote the field of scalars. Our subject is the variation of the spectrum, σ(A) under structured perturbations of the form
$$ A \rightsquigarrow {A_\Delta } = A + B\Delta C,\,\,\Delta \in \mathcal{L}\left( {Y,U} \right) $$
(23.1)
where D(A Δ) = D(A). The operators B, C are fixed and describe both the structure and unboundedness of the perturbations, whilst Δ ∈ ℒ (Y, U) is arbitrary. If U = X = X = Y, B = I x = C, i.e. A Δ = A + Δ, Δ ∈ ℒ (X) the perturbations are bounded and are said to be unstructured.

Keywords

Stability Radius Structure Perturbation Closed Linear Operator Dimensional Linear Subspace Finite Dimensional System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • E. Gallestey
    • 1
  • D. Hinrichsen
    • 1
  • A. J. Pritchard
    • 2
  1. 1.Institut für Dynamische SystemeUniversität BremenBremenGermany
  2. 2.Mathematics DepartmentUniversity of WarwickCoventryUK

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