Journal of Applied Mathematics
Volume 2012 (2012), Article ID 214609, 14 pages
http://dx.doi.org/10.1155/2012/214609
Research Article

Some New Difference Inequalities and an Application to Discrete-Time Control Systems

Hong Zhou,1 Deqing Huang,2 Wu-Sheng Wang,1 and Jian-Xin Xu2

1Department of Mathematics, Hechi University, Guangxi, Yizhou 546300, China
2Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583

Received 1 July 2012; Accepted 17 September 2012

Academic Editor: Jong Hae Kim

Copyright © 2012 Hong Zhou 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

Two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.