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Lyapunov function construction for nonlinear stochastic dynamical systems. (English) Zbl 1284.93207
Summary: 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.

MSC:
93D30 Lyapunov and storage functions
93E03 Stochastic systems in control theory (general)
93E15 Stochastic stability in control theory
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