Mathematical Problems in Engineering 
Volume 2005 (2005), Issue 1, Pages 87-99
doi:10.1155/MPE.2005.87

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

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.