Lyapunov function method for analyzing stability of quasi-Hamiltonian systems under combined Gaussian and Poisson white noise excitations

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• 作者：Weiyan Liu ; Weiqiu Zhu
• 关键词：Quasi ; Hamiltonian system ; Combined Gaussian and Poisson white noise excitations ; Stochastic stability ; Lyapunov function ; Stochastic averaging
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：81
• 期：4
• 页码：1879-1893
• 全文大小：856 KB
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• 作者单位：Weiyan Liu (1) (2)
  Weiqiu Zhu (2)
  
  1. School of Mathematics and Statistics, Taishan University, Tai鈥檃n, 271021, China
  2. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

The asymptotic Lyapunov stability with probability one of multi-degree-of-freedom quasi-Hamiltonian systems subject to parametric excitations of combined Gaussian and Poisson white noises is studied by using Lyapunov function method. According to the integrability and resonance, quasi-Hamiltonian systems can be divided into five classes, namely quasi-non-integrable, quasi-completely integrable and non-resonant, quasi-completely integrable and resonant, quasi-partially integrable and non-resonant, and quasi-partially integrable and resonant. Lyapunov functions for these five classes of systems are constructed. The derivatives for these Lyapunov functions with respect to time are obtained by using the stochastic averaging method. The approximately sufficient condition for the asymptotic Lyapunov stability with probability one of quasi-Hamiltonian system under parametric excitations of combined Gaussian and Poisson white noises is determined based on a theorem due to Khasminskii. Four examples are given to illustrate the application and efficiency of the proposed method. And the results are compared with the corresponding necessary and sufficient condition obtained by using the largest Lyapunov exponent method.