留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

弱耦合双自由度线性非自治随机系统的准确定稳定条件

马天伟

马天伟. 弱耦合双自由度线性非自治随机系统的准确定稳定条件[J]. 应用数学和力学, 2010, 31(8): 986-991. doi: 10.3879/j.issn.1000-0887.2010.08.011
引用本文: 马天伟. 弱耦合双自由度线性非自治随机系统的准确定稳定条件[J]. 应用数学和力学, 2010, 31(8): 986-991. doi: 10.3879/j.issn.1000-0887.2010.08.011
MA Tian-wei. Almost Sure Stability Condition of Weakly Coupled Two-DOF Linear Nonautonomous Random Systems[J]. Applied Mathematics and Mechanics, 2010, 31(8): 986-991. doi: 10.3879/j.issn.1000-0887.2010.08.011
Citation: MA Tian-wei. Almost Sure Stability Condition of Weakly Coupled Two-DOF Linear Nonautonomous Random Systems[J]. Applied Mathematics and Mechanics, 2010, 31(8): 986-991. doi: 10.3879/j.issn.1000-0887.2010.08.011

弱耦合双自由度线性非自治随机系统的准确定稳定条件

doi: 10.3879/j.issn.1000-0887.2010.08.011
基金项目: 美国国家科学基金资助项目(CMMI0758632)
详细信息
  • 中图分类号: O325

Almost Sure Stability Condition of Weakly Coupled Two-DOF Linear Nonautonomous Random Systems

  • 摘要: 研究了参数激励下的二阶振动系统准确定稳定的充分条件.假设该系统由二个弱耦合的子系统所组成,外加激励作用是稳定的遍历性随机过程.使用二次型性质,得到该系统的特征值边界,以及封闭形式的准确定稳定的充分条件.
  • [1] Khasminskii R Z. The Stability of System of Differential Equations Under Random Disturbance of Its Parameters[M]. Moscow: Nauka, 1969. (in Russian)
    [2] Kushner H J. Stochastic Stability and Control[M]. London, New York: Academic Press, 1967.
    [3] Astrom K J. Introduction to Stochastic Control Theory[M]. New York: Dover Publications, 2006.
    [4] Bellman R. Stability Theory of Differential Equations[M]. New York: Dover Publications, 1969.
    [5] Infante E F. On the stability of some linear nonautonomous random systems[J]. ASME Journal of Applied Mechanics, 1968, 35: 7-12. doi: 10.1115/1.3601177
    [6] Kozin F, Wu C M. On the stability of linear stochastic differential equations[J]. ASME Journal of Applied Mechanics, 1973, 40: 87-92. doi: 10.1115/1.3422979
    [7] Ariaratnam S T, Ly B L. The almost-sure stability of some linear stochastic systems[J]. ASME Journal of Applied Mechanics, 1989, 56:175-178. doi: 10.1115/1.3176041
    [8] Ariaratnam S T, Xie W C. Effect of correlation on the almost-sure asymptotic stability of second-order linear stochastic systems[J]. ASME Journal of Applied Mechanics, 1989, 56(3): 685-690. doi: 10.1115/1.3176147
    [9] Ariaratnam S T, Tam D S F, Xie W C. Lyapunov exponents and stochastic stability of coupled linear systems under white noise excitation [J]. Probabilistic Engineering Mechanics, 1991, 6(2) :51-56. doi: 10.1016/0266-8920(91)90017-X
    [10] Ariaratnam S T, Xie W C. Lyapunov exponents and stochastic stability of coupled linear systems under real noise excitations[J]. ASME Journal of Applied Mechanics, 1992, 59(3): 664-673. doi: 10.1115/1.2893775
    [11] Huang Z L, Zhu W Q. Lyapunov exponent and almost sure asymptotic stability of quasi-linear gyroscopic systems[J]. International Journal of Non-Linear Mechanics, 2000, 35(4): 645-655. doi: 10.1016/S0020-7462(99)00047-5
    [12] Ariaratnam S T, Abdelrahman N M. Stochastic stability of non-gyroscopic viscoelastic systems[J]. International Journal of Solids and Structures, 2004, 41(9/10): 2685-2709. doi: 10.1016/j.ijsolstr.2003.11.017
    [13] Merkin D R. Introduction to the Theory of Stability[M]. New York: Spring-Vergla, 1996.
    [14] Wolkowicz H, Styan G P. Bounds for eigenvalues using traces[J]. Linear Algebra and Its Applications, 1980, 29: 471-506. doi: 10.1016/0024-3795(80)90258-X
  • 加载中
计量
  • 文章访问数:  1257
  • HTML全文浏览量:  64
  • PDF下载量:  709
  • 被引次数: 0
出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-04-30
  • 刊出日期:  2010-08-15

目录

    /

    返回文章
    返回