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Stabilization of a Four-Dimensional System under Real Noise Excitation

  • J. Zhu
  • W.-C. Xie
  • R.M.C. So

Keywords

Lyapunov Exponent Maximal Lyapunov Exponent Real Noise Fredholm Alternative Linear Stochastic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Arnold, L.: A formula connecting sample and moment stability of linear stochastic systems. SIAM J. Appl. Math., 44, 793–802 (1984).MATHCrossRefMathSciNetGoogle Scholar
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    Arnold, L., Kliemann, W., Oeljeklaus, E.: Lyapunov exponents of linear stochastic systems. In: Arnold, L., Wihstutz, V. (eds.), Lyapunov Exponents. Springer, Berlin (1986).Google Scholar
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    Arnold, L., Oeljeklaus, E., Pardoux, E.: Almost sure and moment stability for linear Itô equations. In: Arnold, L., Wihstutz, V. (eds.), Lyapunov Exponents. Springer, Berlin (1986).Google Scholar
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    Pardoux, E., Wihstutz, V.: Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion. SIAM J. Appl. Math., 48, 442–457 (1988).MATHCrossRefMathSciNetGoogle Scholar
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    Xie, W.-C.: Moment Lyapunov exponents of a two-dimensional system in wind-induced vibration under real noise excitation. Chaos, Solitons and Fractals, 14, 349–367 (2002).MATHCrossRefMathSciNetGoogle Scholar
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    Xie, W.-C.: Dynamic Stability of Structures. Cambridge University Press, New York (2006).MATHGoogle Scholar
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    Zauderer, E.: Partial Differential Equations of Applied Mathematics, 2nd ed. Wiley, New York (1989).MATHGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • J. Zhu
    • 1
  • W.-C. Xie
    • 1
  • R.M.C. So
    • 2
  1. 1.University of WaterlooCanada
  2. 2.The Hong Kong Polytechnic UniversityHong Kong

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