Copyright © 2010 Hernán R. Henríquez and Claudio Cuevas. 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.
Approximate controllability for semilinear abstract discrete-time systems is
considered. Specifically, we consider the semilinear discrete-time system
, , where are
bounded linear operators acting on a Hilbert space , are -valued bounded
linear operators defined on a Hilbert space , and is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system implies the approximate controllability of the semilinear system.