Impulsive Control of Discrete Systems With Time Delay

被引：101

作者：

Zhang, Yu ^{[1
]}

Sun, Jitao ^{[1
]}

Feng, Gang ^{[2
]}

机构：

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] City Univ Hong Kong, Dept Mfg Engn & Engn Management, Kowloon, Hong Kong, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2009年 / 54卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Discrete system; impulsive control; Lyapunov functional; Razumikhin technique; stability; time delay; DIFFERENTIAL-EQUATIONS; EXPONENTIAL STABILITY; ASYMPTOTIC STABILITY; STABILIZATION;

D O I：

10.1109/TAC.2008.2010968

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This note deals with impulsive control of discrete systems with time delay. It's the first time that an impulsive controller was introduced for discrete systems with time delay. Firstly, some stability criteria for delay discrete systems with impulse effects are obtained by using Lyapunov functionals and Razumikhin technique. These stability criteria show that if the impulses satisfy some conditions, then the original stable systems can keep their stability property even with impulse effects. Then by using Lyapunov functionals or Lyapunov functions together with Razumikhin technique, two stability criteria for the discrete systems with time delay under impulsive control are given. These two results show that unstable systems can be stable under impulsive control. Some examples are also presented to illustrate the efficiency of the obtained results.

引用

页码：871 / 875

页数：5

共 20 条

[1] Uniform asymptotic stability in nonlinear Volterra discrete systems [J].

Eloe, PW ;

Islam, MN ;

Raffoul, YN .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (6-9) :1033-1039

[2] Green's functions and comparison results for impulsive integro differential equations [J].

Franco, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (08) :5723-5728

[3] On hybrid impulsive and switching systems and application to nonlinear control [J].

Guan, ZH ;

Hill, DJ ;

Shen, XM .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (07) :1058-1062

[4] Robust decentralized stabilization for a class of large-scale time-delay uncertain impulsive dynamical systems [J].

Guan, ZH ;

Chen, GR ;

Yu, XH ;

Qin, Y .

AUTOMATICA, 2002, 38 (12) :2075-2084

[5] Absolute stability of time-delay systems with sector-bounded nonlinearity [J].

Han, QL .

AUTOMATICA, 2005, 41 (12) :2171-2176

[6] Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions [J].

He, ZM ;

Zhang, XM .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 156 (03) :605-620

[7] Robust backstepping control for a class of time delayed systems [J].

Hua, CC ;

Guan, XP ;

Shi, P .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (06) :894-899

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

Khadra, A ;

Liu, XZ ;

Shen, X .

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

[9]

Li SL, 2006, DYNAM CONT DIS SER A, V13, P2101

[10]

NIGMATULIN RM, 2003, P INT C PHYS CONTR, V1, P313

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