Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods

被引：131
作者：
Dashkovskiy, Sergey [2 ]
Kosmykov, Michael [1 ]
Mironchenko, Andrii [1 ]
Naujok, Lars [1 ]
机构：
[1] Univ Bremen, Ctr Ind Math, D-28334 Bremen, Germany
[2] Univ Appl Sci Erfurt, Dept Civil Engn, Erfurt, Germany
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2012年 / 6卷 / 03期
关键词：
Impulsive systems; Large-scale systems; Lyapunov methods; Input-to-state stability; Time delays; SMALL-GAIN THEOREM; TO-STATE STABILITY; NETWORKED CONTROL-SYSTEMS; ISS SYSTEMS; DIFFERENTIAL EQUATIONS; HYBRID SYSTEMS; STABILIZATION;
D O I：
10.1016/j.nahs.2012.02.001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we consider the input-to-state stability (ISS) of impulsive control systems with and without time delays. We prove that, if the time-delay system possesses an exponential Lyapunov-Razumikhin function or an exponential Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time delays and prove that the whole network is uniformly ISS under the small-gain and the average dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems, a Lyapunov-Krasovskii functional or a Lyapunov-Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples. (c) 2012 Elsevier Ltd. All rights reserved.
引用
收藏
页码：899 / 915
页数：17
相关论文
共 35 条
  • [1] [Anonymous], 1993, INTRO FUNCTIONAL DIF, DOI 10.1007/978-1-4612-4342-7
  • [2] Ballinger G, 1999, DYN CONTIN DISCRET I, V5, P579
  • [3] Characterizations of input-to-state stability for hybrid systems
    Cai, Chaohong
    Teel, Andrew R.
    [J]. SYSTEMS & CONTROL LETTERS, 2009, 58 (01) : 47 - 53
  • [4] Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays
    Chen, Wu-Hua
    Zheng, Wei Xing
    [J]. AUTOMATICA, 2009, 45 (06) : 1481 - 1488
  • [5] Dashkovskiy S., 2011, P 18 IFAC WORLD C MI, P11018
  • [6] Dashkovskiy S., 2010, P 19 INT S MATH THEO, P1179
  • [7] DASHKOVSKIY S, 2006, P 17 INT S MATH THEO, P77
  • [8] An ISS small gain theorem for general networks
    Dashkovskiy, Sergey
    Rueffer, Bjoern S.
    Wirth, Fabian R.
    [J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2007, 19 (02) : 93 - 122
  • [9] Stability of networks of hybrid ISS systems
    Dashkovskiy, Sergey
    Kosmykov, Michael
    [J]. PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 3870 - 3875
  • [10] SMALL GAIN THEOREMS FOR LARGE SCALE SYSTEMS AND CONSTRUCTION OF ISS LYAPUNOV FUNCTIONS
    Dashkovskiy, Sergey N.
    Rueffer, Bjoern S.
    Wirth, Fabian R.
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (06) : 4089 - 4118
1234