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Prescribed-time stability of stochastic nonlinear delay systems

Author

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  • Xie, Liheng
  • Liu, Shutang
  • Zhu, Xingao

Abstract

This paper investigates the prescribed-time stability and stabilization problem for stochastic nonlinear delay systems. We introduce a new definition of prescribed-time mean-square stability which includes stability in probability and prescribed-time convergence to zero. Utilizing the prescribed-time adjustment function and some stochastic analysis techniques, we establish Lyapunov theorems of prescribed-time mean-square stability for stochastic nonlinear delay systems. An appealing feature of the new theorems is that the solution of prescribed-time stable stochastic nonlinear delay systems can converge to zero at any preset time irrespective of initial data and design parameters. Moreover, under the local Lipschitz condition and the Khasminskii-type condition, we prove that the controlled stochastic nonlinear delay system has a unique solution and achieves prescribed-time mean-square stability. Two simulation examples demonstrate the effectiveness of the theoretical analysis.

Suggested Citation

  • Xie, Liheng & Liu, Shutang & Zhu, Xingao, 2025. "Prescribed-time stability of stochastic nonlinear delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
  • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001298
    DOI: 10.1016/j.chaos.2025.116116
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    References listed on IDEAS

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    1. Liu, Jie & Chen, Guici & Wen, Shiping & Zhu, Song, 2024. "Finite-time piecewise control for discrete-time stochastic nonlinear time-varying systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Xia, Yu & Xiao, Ke & Geng, Zhibo, 2024. "Event-based adaptive fuzzy control for stochastic nonlinear systems with prescribed performance," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Yang, Xuetao & Zhu, Quanxin, 2024. "Stabilization of stochastic nonlinear systems via double-event-triggering mechanisms and switching controls," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    4. Guo, Wanying & Meng, Shuyu & Qi, Ruotong & Li, Wenxue & Wu, Yongbao, 2024. "Existence of stationary distribution for stochastic coupled nonlinear strict-feedback systems with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
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