Mathematical Problems in Engineering
Volume 2005 (2005), Issue 1, Pages 87-99

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

Joseph J. Yamé

Service d'Automatique et Analyse des Systèmes, Université Libre de Bruxelles, Bruxelles 1050, Belgium

Received 20 March 2004; Revised 25 June 2004

Copyright © 2005 Joseph J. Yamé. 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.


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.