Advances in Difference Equations
Volume 2010 (2010), Article ID 869608, 24 pages
Research Article

Stability of Difference Equations and Applications to Robustness Problems

Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, C. Coposu Blvd. No. 4, 300223 Timişoara, Romania

Received 3 November 2009; Accepted 23 February 2010

Academic Editor: Alberto Cabada

Copyright © 2010 Bogdan Sasu. 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.


The aim of this paper is to obtain new necessary and sufficient conditions for the uniform exponential stability of variational difference equations with applications to robustness problems. We prove characterizations for exponential stability of variational difference equations using translation invariant sequence spaces and emphasize the importance of each hypothesis. We introduce a new concept of stability radius rstab(A;B,C) for a variational system of difference equations (A) with respect to a perturbation structure (B,C) and deduce a very general estimate for the lower bound of rstab(A;B,C). All the results are obtained without any restriction concerning the coefficients, being applicable for any system of variational difference equations.