NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY OF IMPULSIVE SWITCHED LINEAR SYSTEMS

被引：4

作者：

Xu, Honglei ^{[1
,2
]}

Teo, Kok Lay ^{[2
]}

Gui, Weihua ^{[1
]}

机构：

[1] Cent S Univ, Sch Informat Sci & Engn, Changsha 410083, Peoples R China

[2] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2011年 / 16卷 / 04期

关键词：

Impulsive switched linear systems; stability analysis; state transition matrix; STABILIZABILITY; CONTROLLABILITY; REACHABILITY; CRITERIA;

D O I：

10.3934/dcdsb.2011.16.1185

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition (IST) matrix. Then, based on the IST matrix and Lyapunov stability theory, necessary and sufficient conditions for the uniform stability, uniform asymptotic stability, and exponential stability of impulsive switched linear systems are established. These stability conditions require the testing on the IST matrix of the impulsive switched linear systems. The results can be reduced to those for switched linear systems without impulsive effects, and also to those for impulsive linear systems without switchings.

引用

页码：1185 / 1195

页数：11

共 17 条

[1]

[Anonymous], 2005, COMM CONT E

[2] Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach [J].

Daafouz, J ;

Riedinger, P ;

Iung, C .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (11) :1883-1887

[3] Perspectives and results on the stability and stabilizability of hybrid systems [J].

DeCarlo, RA ;

Branicky, MS ;

Pettersson, S ;

Lennartson, B .

PROCEEDINGS OF THE IEEE, 2000, 88 (07) :1069-1082

[4] Stability of a contact task for a robotic arm modelled as a switched system [J].

Doulgeri, Z. ;

Iliadis, G. .

IET CONTROL THEORY AND APPLICATIONS, 2007, 1 (03) :844-853

[5]

EZZINE J, 1989, INT J CONTROL, V49, P2045

[6]

Jiang GR, 2006, DISCRETE CONT DYN-B, V6, P1301

[7] THE CONTROL OF SWITCHING DC-DC CONVERTERS - A GENERAL LQR PROBLEM [J].

LEUNG, FHF ;

TAM, PKS ;

LI, CK .

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 1991, 38 (01) :65-71

[8]

Liberzon Daniel, 2003, SWITCHING SYSTEMS CO, V190

[9] Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results [J].

Lin, Hai ;

Antsaklis, Panos J. .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (02) :308-322

[10]

Paul T, 2006, DISCRETE CONT DYN-B, V6, P1191

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