On the Existence and Construction of Common Lyapunov Functions for Switched Discrete Systems

被引：0
|
作者：
Kosov A.A. [1 ]
Kozlov M.V. [2 ]
机构：
[1] Matrosov Institute for System Dynamics and Control Theory, ul. Lermontova 134, Irkutsk
[2] National Research Mordovian State University, ul. Bol’shevistskaya 68, Saransk
来源：
Journal of Applied and Industrial Mathematics | 2018年 / 12卷 / 4期
基金：
俄罗斯基础研究基金会;
关键词：
common Lyapunov function; stability; switched discrete system;
D O I：
10.1134/S1990478918040075
中图分类号：
学科分类号：
摘要：
Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach. © 2018, Pleiades Publishing, Ltd.
引用
收藏
页码：668 / 677
页数：9
相关论文
共 50 条
  • [1] Existence of Common Lyapunov Functions for Infinite-Dimensional Switched Linear Systems
    Hante, Falk M.
    Sigalotti, Mario
    [J]. 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, : 5668 - 5673
  • [2] Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems
    Sun, C.
    Fang, B.
    Huang, W.
    [J]. IET CONTROL THEORY AND APPLICATIONS, 2011, 5 (03): : 535 - 537
  • [3] Common polynomial Lyapunov functions for linear switched systems
    Mason, P
    Boscain, U
    Chitour, Y
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (01) : 226 - 245
  • [4] On the existence of common Lyapunov triples for ISS and iISS switched systems
    Mancilla-Aguilar, JL
    García, RA
    [J]. PROCEEDINGS OF THE 39TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2000, : 3507 - 3512
  • [5] On Common Quadratic Lyapunov Functions for Dynamic Normal Switched Systems
    Eisenbarth, Geoffrey
    Davis, John M.
    Gravagne, Ian
    [J]. 45TH SOUTHEASTERN SYMPOSIUM ON SYSTEM THEORY, 2013, : 108 - 113
  • [6] A result on the existence of common quadratic Lyapunov functions for pairs of stable discrete-time LTI systems
    Mason, O
    Shorten, R
    [J]. PROCEEDINGS OF THE 2003 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2003, : 4471 - 4475
  • [7] Construction of the Lyapunov functions for discrete random-parameter systems
    Barabanov, IN
    [J]. AUTOMATION AND REMOTE CONTROL, 1995, 56 (11) : 1529 - 1537
  • [8] Common and Multiple Lyapunov Functions in Stability Analysis of Nonlinear Switched Systems
    Vassilyev, S. N.
    Kosov, A. A.
    [J]. 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES (ICNPAA 2012), 2012, 1493 : 1066 - 1073
  • [9] Common joint linear copositive Lyapunov functions for positive switched systems
    Wu, Zhaorong
    Sun, Yuangong
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2014, 351 (05): : 2504 - 2514
  • [10] Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions
    Blanchini, Franco
    Savorgnan, Carlo
    [J]. PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 122 - +
12345