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.

Abstract

Approximate controllability for semilinear abstract discrete-time systems is considered. Specifically, we consider the semilinear discrete-time system xk+1=Akxk+f(k,xk)+Bkuk, k∈ℕ0, where Ak are bounded linear operators acting on a Hilbert space X, Bk are X-valued bounded linear operators defined on a Hilbert space U, and f is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system xk+1=Akxk+Bkuk implies the approximate controllability of the semilinear system.