On the stability of switched positive linear systems

被引：287
作者：
Gurvits, L. [1 ]
Shorten, R.
Mason, O.
机构：
[1] Los Alamos Natl Lab, Los Alamos, NM 87545 USA
[2] NUI Maynooth, Hamilton Inst, Maynooth, Kildare, Ireland
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2007年 / 52卷 / 06期
基金：
爱尔兰科学基金会;
关键词：
positive linear systems; stability theory; switched linear systems;
D O I：
10.1109/TAC.2007.899057
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this note, we show that 1) this conjecture is true for systems constructed from a pair of second-order Metzler matrices; 2) the conjecture is true for systems constructed from an arbitrary finite number of second-order Metzler matrices; and 3) the conjecture is in general false for higher order systems. The implications of our results, both for the design of switched positive linear systems, and for research directions that arise as a result of our work, are discussed toward the end of the note.
引用
收藏
页码：1099 / 1103
页数：5
相关论文
共 20 条
  • [1] Conditions on the stability of a class of second-order switched systems
    Akar, M
    Paul, A
    Safonov, MG
    Mitra, U
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (02) : 338 - 340
  • [2] [Anonymous], 2003, 2 EIGENVALUE GOOGLE
  • [3] [Anonymous], POSITIVE LINEAR SYST
  • [4] Berman A., 1994, SIAM Classics in Applied Mathe- matics
  • [5] A converse Lyapunov theorem for a class of dynamical systems which undergo switching
    Dayawansa, WP
    Martin, CF
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1999, 44 (04) : 751 - 760
  • [6] GURVITS L, 1995, LINEAR ALGEBRA APPL, V231, P47, DOI 10.1016/0024-3795(94)00010-7
  • [7] GURVITS L, 2003, P IEEE C DEC CONTR M
  • [8] GURVITS L, 2002, P MTNS 2002
  • [9] Horn R.A., 1991, TOPICS MATRIX ANAL
  • [10] Coordination of groups of mobile autonomous agents using nearest neighbor rules
    Jadbabaie, A
    Lin, J
    Morse, AS
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (06) : 988 - 1001
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