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Lyapunov function construction for nonlinear stochastic dynamical systems

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Abstract

Though the Lyapunov function method is more efficient than the largest Lyapunov exponent method in evaluating the stochastic stability of multi-degree-of-freedom (MDOF) systems, the construction of Lyapunov function is a challenging task. In this paper, a specific linear combination of subsystems’ energies is proposed as Lyapunov function for MDOF nonlinear stochastic dynamical systems, and the corresponding sufficient condition for the asymptotic Lyapunov stability with probability one is then determined. The proposed procedure to construct Lyapunov function is illustrated and validated with several representative examples, where the influence of coupled/uncoupled dampings and excitation intensities on stochastic stability is also investigated.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (Grant no. 11025211, 11002077, 11202181), the Zhejiang Provincial Natural Science Foundation of China (Grant no. Z6090125, LQ12A02001), the Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20110101110050), and the special fund for national excellent Ph.D. dissertation.

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Correspondence to Z. L. Huang.

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Ling, Q., Jin, X.L., Wang, Y. et al. Lyapunov function construction for nonlinear stochastic dynamical systems. Nonlinear Dyn 72, 853–864 (2013). https://doi.org/10.1007/s11071-013-0757-3

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  • DOI: https://doi.org/10.1007/s11071-013-0757-3

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