Spectral Theory for Neutral Delay Equations with Applications to Control and Stabilization

  • Sjoerd M. Verduyn Lunel
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 134)

Abstract

For dynamical systems governed by feedback laws, time delays arise naturally in the feedback loop to represent effects due to communication, transmission, transportation or iternia effects. The introduction of time delays in a system of differential equations results in an infinite dimensional state space. The solution operator associated with a differential delay equation is a nonself-adjoint operator defined on a Banach space. This implies that general abstract theorems cannot directly be applied. In this paper we discuss the spectral properties of neutral differential delay equations, series expansions of solutions, completeness of eigenvectors and generalized eigenvectors, solutions of neutral delay equations that decay faster than any exponential, and applications to control and stabilization.

Key words

completeness F-completeness neutral delay equation robustness sensitivity small solutions small delays stabilizability. 
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Copyright information

© Springer-Verlag New York, Inc. 2003

Authors and Affiliations

  • Sjoerd M. Verduyn Lunel
    • 1
  1. 1.Mathematisch InstituutUniversiteit LeidenRA LeidenThe Netherlands

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