Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (8): 1033-1038.doi: https://doi.org/10.1007/s10483-010-1339-x

• Articles • 上一篇    下一篇

Almost sure stability condition of weakly coupled linear nonautonomous random systems

 T.W.MA   

  1. Department of Civil and Environmental Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA
  • 收稿日期:2009-10-04 修回日期:2010-04-30 出版日期:2010-07-23 发布日期:2010-08-01

Almost sure stability condition of weakly coupled linear nonautonomous random systems

 T.W.MA   

  1. Department of Civil and Environmental Engineering, University of Hawaii at Manoa, Honolulu, HI 96822, USA
  • Received:2009-10-04 Revised:2010-04-30 Online:2010-07-23 Published:2010-08-01

摘要: In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.

Abstract: In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.

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