中国物理B ›› 2001, Vol. 10 ›› Issue (6): 480-485.doi: 10.1088/1009-1963/10/6/303

• GENERAL • 上一篇    下一篇

THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS

尚玫1, 郭永新2   

  1. (1)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Physics, Liaoning University, Shenyang 110036, China
  • 收稿日期:2000-10-27 修回日期:2001-02-15 出版日期:2005-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Natural Science Foundation of Liaoning Province of China (Grant No. 002083) and by the Science Research Foundation of Liaoning Education Commission of China (Grant Nos. 990111004, 20021004).

THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS

Shang Mei (尚玫)a, Guo Yong-xin (郭永新)b   

  1. a Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Liaoning University, Shenyang 110036, China
  • Received:2000-10-27 Revised:2001-02-15 Online:2005-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the Natural Science Foundation of Liaoning Province of China (Grant No. 002083) and by the Science Research Foundation of Liaoning Education Commission of China (Grant Nos. 990111004, 20021004).

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摘要： We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.

Abstract: We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.

Key words: stochastic nonholonomic system, mean-square exponential stability and instability

中图分类号:  (Stochastic analysis methods)

  • 05.10.Gg
05.40.Ca (Noise) 02.50.Cw (Probability theory) 02.50.Ey (Stochastic processes)