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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 206343, 7 pages
Research Article

Exponential Stability Criteria for Nonautonomous Difference Systems

Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla Postal 933, 5290000 Osorno, Chile

Received 28 January 2014; Revised 25 March 2014; Accepted 9 April 2014; Published 29 April 2014

Academic Editor: Henryk Hudzik

Copyright © 2014 Rigoberto Medina. 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 characterize the exponential stability of linear systems of difference equations with slowly varying coefficients. Our approach is based on the generalization of the freezing method for difference equations combined with new estimates for the norm of bounded linear operators. The main novelty of this work is that we use estimates for the absolute values of entries of a matrix-valued function, instead of bounds on its eigenvalues. By this method, new explicit stability criteria for linear nonautonomous systems are derived.