Exponential stability of nonlinear time-delay systems with delayed impulse effects

被引：228

作者：

Chen, Wu-Hua ^{[1
,2
]}

Zheng, Wei Xing ^{[1
]}

机构：

[1] Univ Western Sydney, Sch Comp & Math, Penrith, NSW 2751, Australia

[2] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Guangxi, Peoples R China

来源：

AUTOMATICA | 2011年 / 47卷 / 05期

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Impulsive systems; Delayed impulses; Exponential stability; H-INFINITY-CONTROL; DESIGN;

D O I：

10.1016/j.automatica.2011.02.031

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The problem of exponential stability for nonlinear time-delay systems with delayed impulses is addressed in this paper. Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for two kinds of delayed impulses (i.e., destabilizing delayed impulses and stabilizing delayed impulses). It is shown that if a nonlinear impulsive time-delay system without impulse input delays is exponentially stable, then under some conditions, its stability is robust with respect to small impulse input delays. Moreover, it is also shown that for a stable nonlinear impulsive time-delay system, if the magnitude of the delayed impulses is sufficiently small, then under some conditions, the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays. The efficiency of the proposed results is illustrated by three numerical examples. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1075 / 1083

页数：9

共 23 条

[1] EXPONENTIAL STABILITY OF LINEAR DELAY IMPULSIVE DIFFERENTIAL-EQUATIONS [J].

ANOKHIN, A ;

BEREZANSKY, L ;

BRAVERMAN, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 193 (03) :923-941

[2]

Bainov D.D., 1989, Systems with Impulse Effect

[3]

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

[4]

Bernstein D. S., 2005, MATRIX MATH THEORY F

[5] Robust H∞ control of uncertain linear impulsive stochastic systems [J].

Chen, Wu-Hua ;

Wang, Jun-Ge ;

Tang, You-Jian ;

Lu, Xiaomei .

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2008, 18 (13) :1348-1371

[6] Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2009, 56 (06) :1248-1259

[7] Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

AUTOMATICA, 2009, 45 (06) :1481-1488

[8] Robust stability and H∞-control of uncertain impulsive systems with time-delay [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

AUTOMATICA, 2009, 45 (01) :109-117

[9]

Guan ZH, 1999, DYN CONTIN DISCRET I, V6, P367

[10] Lyapunov conditions for input-to-state stability of impulsive systems [J].

Hespanha, Joao P. ;

Liberzon, Daniel ;

Teel, Andrew R. .

AUTOMATICA, 2008, 44 (11) :2735-2744

← 1 2 3 →