Similarity to contraction and asymptotics of a class of infinite-dimensional discrete-time systems

Yamé, Joseph J.

doi:https://doi.org/10.1155/MPE.2005.87

Mathematical Problems in Engineering

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Volume 2005 | Article ID 845140 | https://doi.org/10.1155/MPE.2005.87

Similarity to contraction and asymptotics of a class of infinite-dimensional discrete-time systems

Joseph J. Yamé¹

Received20 Mar 2004

Revised25 Jun 2004

Abstract

A class of infinite-dimensional discrete-time state operators is exhibited as concrete instances of power-bounded operators that are not similar to contractions. It is shown that such discrete-time systems arise from sampled feedback control of unstable continuous-time systems. The asymptotic behavior of the state operators of these discrete systems is not intimately related to their spectral radius.

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Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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