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The Almost Sure Asymptotic Stability and p th Moment Asymptotic Stability of Nonlinear Stochastic Differential Systems With Polynomial Growth

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3 Author(s)
Lei Liu ; Department of Control Science and Engineering and the Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, Hubei, China ; Yi Shen ; Feng Jiang

This note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems (SDSs). The systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition. By applying some novel techniques, some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such SDSs. We also provide the range of the order p. A numerical example is provided to illustrate the effectiveness and the benefits of the proposed result.

Published in:

IEEE Transactions on Automatic Control  (Volume:56 ,  Issue: 8 )