Advances in Difference Equations
Volume 2010 (2010), Article ID 695290, 17 pages
Research Article

Approximate Controllability of Abstract Discrete-Time Systems

1Departamento de Matemática, Universidad de Santiago (USACH) Casilla 307, Correo 2, Santiago, Chile
2Departamento de Matemática, Universidade Federal de Pernambuco, Recife, PE 50540-740, Brazil

Received 12 April 2010; Accepted 2 September 2010

Academic Editor: Rigoberto Medina

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 xk+1=Akxk+f(k,xk)+Bkuk, k0, 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.