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
收藏
页码：1185 / 1195
页数：11
相关论文
共 50 条
  • [1] On Necessary and Sufficient Conditions for the Asymptotic Stability of Impulsive Systems
    R. I. Gladilina
    A. O. Ignat'ev
    Ukrainian Mathematical Journal, 2003, 55 (8) : 1254 - 1264
  • [2] New necessary and sufficient conditions for finite-time stability of impulsive switched linear time-varying systems
    Chen, Guopei
    Yang, Ying
    IET CONTROL THEORY AND APPLICATIONS, 2018, 12 (01): : 140 - 148
  • [3] Necessary and sufficient conditions for controllability of switched linear systems
    Xie, GM
    Long, W
    PROCEEDINGS OF THE 2002 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2002, 1-6 : 1897 - 1902
  • [4] Necessary and Sufficient Conditions of Stability for Switched Nonlinear Systems
    Zhu, Liying
    Feng, Gang
    2014 11TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA), 2014, : 2079 - 2084
  • [5] Necessary and sufficient conditions for stability of switched nonlinear systems
    Zhu, Liying
    Feng, Gang
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2015, 352 (01): : 117 - 137
  • [6] ON THE NECESSARY AND SUFFICIENT CONDITIONS FOR THE STABILITY OF LINEAR GENERALIZED ORDINARY DIFFERENTIAL, LINEAR IMPULSIVE AND LINEAR DIFFERENCE SYSTEMS
    Akhalaia, Shota
    Ashordia, Malkhaz
    Kekelia, Nestan
    GEORGIAN MATHEMATICAL JOURNAL, 2009, 16 (04) : 597 - 616
  • [7] Necessary and sufficient conditions for controllability and observability of switched impulsive control systems
    Xie, GM
    Wang, L
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (06) : 960 - 966
  • [8] Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems
    Amato, F.
    De Tommasi, G.
    Pironti, A.
    AUTOMATICA, 2013, 49 (08) : 2546 - 2550
  • [9] Necessary and sufficient conditions for controllability of switched impulsive control systems with time delay
    Xie, Guangming
    Yu, Junyan
    Wang, Long
    PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 4093 - 4098
  • [10] NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY OF LINEAR NONSTATIONARY SYSTEMS
    GIL, MI
    SOVIET JOURNAL OF COMPUTER AND SYSTEMS SCIENCES, 1986, 24 (01): : 155 - 160
12345