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基于向量Liapunov函数不连续系统的稳定性研究

慕小武 程桂芳 丁志帅

慕小武, 程桂芳, 丁志帅. 基于向量Liapunov函数不连续系统的稳定性研究[J]. 应用数学和力学, 2007, 28(12): 1441-1447.
引用本文: 慕小武, 程桂芳, 丁志帅. 基于向量Liapunov函数不连续系统的稳定性研究[J]. 应用数学和力学, 2007, 28(12): 1441-1447.
MU Xiao-wu, CHENG Gui-fang, DING Zhi-shuai. On the Stability of Discontinuous Systems via Vector Liapunov Functions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1441-1447.
Citation: MU Xiao-wu, CHENG Gui-fang, DING Zhi-shuai. On the Stability of Discontinuous Systems via Vector Liapunov Functions[J]. Applied Mathematics and Mechanics, 2007, 28(12): 1441-1447.

基于向量Liapunov函数不连续系统的稳定性研究

详细信息
    作者简介:

    慕小武(1963- ),男,河南温县人,教授(联系人.Tel:+86-371-67762897;Fax:+86-371-67766220;E-mail:muxiaowu@zzu.edu.cn).

  • 中图分类号: O231.2

On the Stability of Discontinuous Systems via Vector Liapunov Functions

  • 摘要: 基于局部Lipschitz连续且正则(Clarke意义下)的向量Liapunov函数,讨论不连续自治系统的稳定性(Filippov解意义下).通过定义一类新的向量Liapunov函数的“集值导数”,给出了关于不连续系统的广义比较原理.基于Lipschitz连续且正则的向量Liapunov函数,进一步的给出不连续自治系统的Liapunov稳定性定理.
  • [1] Filippov A F.Differential equations with discontinuous right-hand side[J].Amer Math Soc Translations,1964,42(2):199-231.
    [2] Shevitz Daniel,Paden Brad.Liapunov stability theory of nonsmooth systems[J].IEEE Transactions on Automatic Control,1994,39(9):1910-1914. doi: 10.1109/9.317122
    [3] Ryan E P.An integral invariance principle for differential inclusions with application in adaptive control[J].SIAM J Control and Optimization,1997,36(3):960-980.
    [4] Bacciottic A,Ceragioli F.Stability and stabilization of discontinuous systems and nonsmooth Liapunov function[J].Esaim Cocv,1999,4(2):361-376. doi: 10.1051/cocv:1999113
    [5] Nersesov S G,Haddad W M.On the stability and control of nonlinear dynamical systems via vector Liapunov functions[J].IEEE Transactions on Automatic Control,2006,51(2):203-215. doi: 10.1109/TAC.2005.863496
    [6] Matrosov V M.Method of vector Liapunov functions of interconnected systems with distributed parameters (survey)[J].Avtomatikai Telemekhanika,1977,33(1):63-75.
    [7] Lakshnikantham V,Matrosov V M,Sivasundaram S.Vector Liapunov Functions and Stability Analysis of Nonlinear Systems[M].Dordrecht, The Netherlands:Kluwer,1991.
    [8] Drici Z.New directions in the method of vector Liapunov functions[J].J Math Anal Appl,1994,184(2):317-325. doi: 10.1006/jmaa.1994.1202
    [9] Kim S J,Ha I J.Existence of caratheodory solutions in nonlinear systems with discontinuous switching feedback controllers[J].IEEE Transactions on Automatic Control,2004,49(7):1167-1171. doi: 10.1109/TAC.2004.831127
    [10] Clarke F H,Ledyaev Yu S,Stern R J,et al.Nonsmooth Analysis and Control Theory[M].Graduate Texts in Mathematics.New York: Springer,1998.
    [11] Bhaskar T Gnana,Devi J Vasundhara.Set differential systems and vector Liapunov functions[J].Applied Mathematics and Computation,2005,165(3):539-548. doi: 10.1016/j.amc.2004.04.074
    [12] Andreyev A S,Peregudova O A.The comparison method in asymptotic stability problems[J].Journal of Applied Mathematics and Mechanics,2006,70(6):865-875. doi: 10.1016/j.jappmathmech.2007.01.006
    [13] 贺建勋.关于不连续系统稳定性的比较原理[J].厦门大学学报(自然科学版), 1982,13(2):117-126.
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出版历程
  • 收稿日期:  2006-07-04
  • 修回日期:  2007-10-12
  • 刊出日期:  2007-12-15

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