Unified Stability Analysis for Ito Stochastic Systems: From Almost Surely Asymptotic to Finite-Time Convergence

• 成果类型: Article
• 署名作者: Luo, Shixian; Deng, Feiqi; Yu, Xinghuo
• 署名单位: Guangxi University; South China University of Technology; Royal Melbourne Institute of Technology (RMIT)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3057990
• 发表日期: 2022
• 页码: 406-412
• 关键词: stochastic systems; CONVERGENCE; Stability criteria; Stochastic processes; Indium tin oxide; asymptotic stability; Lyapunov methods; Almost sure stability; finite-time control; Finite-time convergence; sliding mode control (SMC); Stochastic systems

摘要

This article proposes a unified Lyapunov framework for analyzing the stochastic asymptotic and finite-time convergence/stability for Ito stochastic nonlinear systems. By exploring the coupling effect between the drift and the diffusion parts of the system, novel almost sure convergence/stability criteria are established. For the finite-time case, the stability criteria not only capture the stabilizing effect of stochastic noise but also include the existing finite-time stability criteria as special cases. For the asymptotic case, it removes the local Lipschitz conditions and the nonzero property of the solution demanded by the existing results. The proposed theoretical results are further applied to solve the sliding mode control and the optimal finite-time/asymptotic stabilization problems.