Prescribed-time stability of stochastic nonlinear delay systems

Liheng Xie, Shutang Liu and Xingao Zhu

Chaos, Solitons & Fractals, 2025, vol. 193, issue C

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.

Keywords: Prescribed-time mean-square stability; Stochastic nonlinear delay systems; Prescribed-time adjustment function; Khasminskii-type condition (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001298

DOI: 10.1016/j.chaos.2025.116116

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