A generalized Halanay inequality on impulsive delayed dynamical systems and its applications

被引：11

作者：

Wu, Quanjun ^{[1
,2
,3
]}

Zhang, Hua ^{[1
,2
,4
]}

Xiang, Lan ^{[5
]}

Zhou, Jin ^{[1
,2
]}

机构：

[1] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China

[2] Shanghai Univ, Shanghai Key Lab Mech Energy Engn, Shanghai 200072, Peoples R China

[3] Shanghai Univ Elect Power, Sch Math & Phys, Shanghai 200090, Peoples R China

[4] Tongren Coll, Dept Math & Comp Sci, Tongren 554300, Peoples R China

[5] Shanghai Univ, Sch Sci, Dept Phys, Shanghai 200444, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2012年 / 45卷 / 01期

基金：

美国国家科学基金会;

关键词：

DIFFERENTIAL EQUATIONS; STABILITY ANALYSIS; CHAOTIC SYSTEMS; NEURAL-NETWORKS; SYNCHRONIZATION;

D O I：

10.1016/j.chaos.2011.09.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main objective of this paper is to extend previous results on Halanay inequality for impulsive delayed dynamical systems. Based on the Razumikhin technique, a generalized Halanay differential inequality on impulsive delayed dynamical systems is analytically established. Compared with some existing works, the distinctive feature of this work is that it can be used to stabilize an unstable delayed dynamical system via impulses. The generalized Halanay inequality may be applied to secure communication systems, and a numerical example is given for illustrating and interpreting the theoretical results. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：56 / 62

页数：7

共 16 条

[1]

Baker CH, 1999, VOLTERRA EQUATIONS A, P999

[2]

Ballinger G, 1999, DYN CONTIN DISCRET I, V5, P579

[3]

Gopalsamy K., 2013, STABILITY OSCILLATIO, V74

[4]

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

[5] Impulsively synchronizing chaotic systems with delay and applications to secure communication [J].

Khadra, A ;

Liu, XZ ;

Shen, X .

AUTOMATICA, 2005, 41 (09) :1491-1502

[6] Impulsive synchronization of chaotic systems subject to time delay [J].

Liu, Xinzhi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) :E1320-E1327

[7] The exponential asymptotic stability of singularly perturbed delay differential equations with a hounded lag [J].

Tian, HJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 270 (01) :143-149

[8]

TOKUMARU H., 1975, IFAC P, V8, P592

[9]

Wu QJ, 2009, L N INST COMP SCI SO, V4, P1124

[10] Attracting and invariant sets for a class of impulsive functional differential equations [J].

Xu, Daoyi ;

Yang, Zhichun .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) :1036-1044

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