Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 910936, 19 pages
http://dx.doi.org/10.5402/2011/910936
Research Article

The Stability Cone for a Difference Matrix Equation with Two Delays

1Department of Mathematical Analysis, Chelyabinsk State Pedagogical University, Chelyabinsk 454080, Russia
2Applied Mathematics Department, South Ural State University, Chelyabinsk 454080, Russia
3Faculty of Applied Mathematics and Mechanics, Perm State Technical University, Perm 614990, Russia

Received 30 March 2011; Accepted 25 April 2011

Academic Editors: E. Karpov, G. Mishuris, and Y. Qin

Copyright © 2011 S. A. Ivanov et al. 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 provide geometric algorithms for checking the stability of matrix difference equations π‘₯ 𝑛 = 𝐴 π‘₯ 𝑛 βˆ’ π‘š + 𝐡 π‘₯ 𝑛 βˆ’ π‘˜ with two delays π‘š , π‘˜ such that the matrix 𝐴 𝐡 βˆ’ 𝐡 𝐴 is nilpotent. We give examples of how our results can be applied to the study of the stability of neural networks.