Advances in Difference Equations
Volume 2008 (2008), Article ID 396504, 14 pages
doi:10.1155/2008/396504
Research Article
Absolute Stability of Discrete-Time Systems with Delay
Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile
Received 18 October 2007; Accepted 22 November 2007
Academic Editor: Bing Gen Zhang
Copyright © 2008 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.
Abstract
We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the “freezing” technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.