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Volume 9 Issue 6
Jun.  2022

IEEE/CAA Journal of Automatica Sinica

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H. F. Min, S. Y. Xu, B. Y. Zhang, Q. Ma, and  D. M. Yuan,  “Fixed-time Lyapunov criteria and state-feedback controller design for stochastic nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1005–1014, Jun. 2022. doi: 10.1109/JAS.2022.105539
Citation: H. F. Min, S. Y. Xu, B. Y. Zhang, Q. Ma, and  D. M. Yuan,  “Fixed-time Lyapunov criteria and state-feedback controller design for stochastic nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1005–1014, Jun. 2022. doi: 10.1109/JAS.2022.105539

Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems

doi: 10.1109/JAS.2022.105539
Funds:  This work was supported in part by the National Natural Science Foundation of China (62073166, 61673215), and the Key Laboratory of Jiangsu Province
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  • This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems. We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure. In particular, an important corollary is obtained, which can give a less conservative upper-bound estimate of the settling time. Based on the backstepping technique and the addition of a power integrator method, a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems. It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria. Finally, the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.

     

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    Highlights

    • An improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure is proposed
    • A less conservative upper-bound estimate of the settling time is proved and obtained
    • A state-feedback controller is constructed by using backstepping, the adding a power integrator method and the fixed-time control procedure
    • The property of fixed-time stability in probability is obtained

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