P‐moment stability under small Gauss type random excitation of stochastic system | Zendy

Lu Zhanhui | Zendy; Hao Zhiqi | Zendy; Zhao Weixiang | Zendy; Xie Di | Zendy

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P‐moment stability under small Gauss type random excitation of stochastic system

Author(s) -

Lu Zhanhui,

Hao Zhiqi,

Zhao Weixiang,

Xie Di

Publication year - 2016

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4146

Subject(s) - mathematics , moment (physics) , stability (learning theory) , gauss , random matrix , isometry (riemannian geometry) , mathematical analysis , type (biology) , order (exchange) , gaussian , matrix (chemical analysis) , second moment of area , lyapunov function , physics , classical mechanics , nonlinear system , eigenvalues and eigenvectors , geometry , quantum mechanics , computer science , ecology , materials science , finance , machine learning , economics , composite material , biology

In this paper, the stochastic stability under small Gauss type random excitation is investigated theoretically and numerically. When p is larger than 0, the p ‐moment stability theorem of stochastic models is proved by Lyapunov method, Ito isometry formula, matrix theory and so on. Then the application of p ‐moment such as k ‐order moment of the origin and k ‐order moment of the center is introduced and analyzed. Finally, p ‐moment stability of the power system is verified through the simulation example of a one machine and infinite bus system. Copyright © 2016 John Wiley & Sons, Ltd.

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