GENERALIZED DISCRETE HALANAY INEQUALITIES AND THE ASYMPTOTIC BEHAVIOR OF NONLINEAR DISCRETE SYSTEMS

被引：5

作者：

Xu, Liguang ^{[1
]}

机构：

[1] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310023, Zhejiang, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2013年 / 50卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Halanay inequality; discrete systems; attracting set; global asymptotic stability; SQUARE EXPONENTIAL STABILITY; DELAY-DIFFERENTIAL SYSTEMS; NEURAL-NETWORKS; GLOBAL STABILITY; SWITCHED SYSTEMS; EQUATIONS; TIME;

D O I：

10.4134/BKMS.2013.50.5.1555

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

引用

页码：1555 / 1565

页数：11

共 25 条

[1]

Agarwal R., 2008, Commun. Appl. Anal, V12, P83

[2]

[Anonymous], MATH ITS APPL

[3] Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag [J].

Baker, Christopher T. H. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (09) :2663-2682

[4]

Beckenbach E. F., 1961, Inequalities

[5] Global dynamics of one class of nonlinear nonautonomous systems with time-varying delays [J].

Berezansky, L. ;

Idels, L. ;

Troib, L. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (18) :7499-7512

[6] Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays [J].

Cao, JD ;

Wang, J .

NEURAL NETWORKS, 2004, 17 (03) :379-390

[7] Robust sampled-data control of a class of semilinear parabolic systems [J].

Fridman, Emilia ;

Blighovsky, Anatoly .

AUTOMATICA, 2012, 48 (05) :826-836

[8]

Gopalsamy K., 2013, STABILITY OSCILLATIO, V74

[9]

Halanay A., 1966, Differential equations: Stability, Oscillations and Time Lags, V6

[10] A note on the global stability of generalized difference equations [J].

Liz, E ;

Ferreiro, JB .

APPLIED MATHEMATICS LETTERS, 2002, 15 (06) :655-659

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