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

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

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 analy...

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Main Authors: Hong Zhou, Deqing Huang, Wu-Sheng Wang, Jian-Xin Xu
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/214609
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spelling doaj-7d75e9b241304b66941532778d0896f82020-11-24T23:37:15ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/214609214609Some New Difference Inequalities and an Application to Discrete-Time Control SystemsHong Zhou0Deqing Huang1Wu-Sheng Wang2Jian-Xin Xu3Department of Mathematics, Hechi University, Guangxi, Yizhou 546300, ChinaDepartment of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117583, SingaporeDepartment of Mathematics, Hechi University, Guangxi, Yizhou 546300, ChinaDepartment of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117583, SingaporeTwo 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.http://dx.doi.org/10.1155/2012/214609
collection DOAJ
language English
format Article
sources DOAJ
author Hong Zhou
Deqing Huang
Wu-Sheng Wang
Jian-Xin Xu
spellingShingle Hong Zhou
Deqing Huang
Wu-Sheng Wang
Jian-Xin Xu
Some New Difference Inequalities and an Application to Discrete-Time Control Systems
Journal of Applied Mathematics
author_facet Hong Zhou
Deqing Huang
Wu-Sheng Wang
Jian-Xin Xu
author_sort Hong Zhou
title Some New Difference Inequalities and an Application to Discrete-Time Control Systems
title_short Some New Difference Inequalities and an Application to Discrete-Time Control Systems
title_full Some New Difference Inequalities and an Application to Discrete-Time Control Systems
title_fullStr Some New Difference Inequalities and an Application to Discrete-Time Control Systems
title_full_unstemmed Some New Difference Inequalities and an Application to Discrete-Time Control Systems
title_sort some new difference inequalities and an application to discrete-time control systems
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/214609
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AT deqinghuang somenewdifferenceinequalitiesandanapplicationtodiscretetimecontrolsystems
AT wushengwang somenewdifferenceinequalitiesandanapplicationtodiscretetimecontrolsystems
AT jianxinxu somenewdifferenceinequalitiesandanapplicationtodiscretetimecontrolsystems
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