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

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. Copyright © 2005 Hindawi Publishing Corporation.SCOPUS: ar.j