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New results on the fourth moment exponentially stable for a class of stochastic nonlinear systems and its application

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Abstract

Under the relaxed triangular-type condition on the drift terms and diffusion terms, this paper investigates the problem of the fourth moment exponentially stable for a class of stochastic nonlinear systems by, respectively, adopting state feedback and output feedback. Based on the Lyapunov stability criterion, the parameter-dependent controller, which is used to compensate for the drift terms and diffusion terms, is constructed such that the closed-loop system is fourth moment exponentially stable. Furthermore, the fourth moment exponential stability of the system states and errors can be guaranteed. Two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grants 61403041 and 61673242, the China Postdoctoral Science Foundation under Grants 2016T90462 and 2015M580435, the Natural Science Foundation of Liaoning Province under Grant 201602007, the Program for Liaoning Excellent Talents in University under Grant LJQ2015001, the Shandong Provincial Natural Science Foundation of China under Grant 2016ZRB01076, and the Jiansu Planned Projects for Postdoctoral Research Funds under Grant 1601218C.

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Authors and Affiliations

  1. College of Engineering, Bohai University, Jinzhou, 121013, China

    Liang Liu

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Liang Liu & Shengyuan Xu

  3. Institute of Automation, Qufu Normal University, Qufu, 273165, China

    Xuejun Xie

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  1. Liang Liu
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  2. Shengyuan Xu
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  3. Xuejun Xie
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Correspondence to Liang Liu.

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Liu, L., Xu, S. & Xie, X. New results on the fourth moment exponentially stable for a class of stochastic nonlinear systems and its application. Nonlinear Dyn 89, 1279–1287 (2017). https://doi.org/10.1007/s11071-017-3515-0

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  • DOI: https://doi.org/10.1007/s11071-017-3515-0

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