发表机构
Research Institute of Intelligent Complex Systems, Fudan University; School of Mathematics Sciences, Fudan University; Department of Mathematics and Statistics, University of Strathclyde（复旦大学智能复杂系统研究院; 复旦大学数学科学学院; 斯特拉斯克莱德大学数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对一般非线性随机系统，在局部Lipschitz系数下，通过足够快的采样实现高概率指数镇定，并针对不同增长阶数分别提出方法。
AI 中文摘要
本文研究在连续时间闭环系统的局部指数型Lyapunov条件下，一般非线性随机系统的采样数据镇定问题。系数仅假设为局部Lipschitz，既不满足线性增长条件，也不满足Khasminskii型条件。两个反例表明，几乎必然镇定通常无法实现。相反，给定初始状态，我们在足够快的采样下建立了具有任意高概率的指数稳定性。针对Lyapunov条件中的增长阶数p≥2和0<p<2，分别开发了不同的方法。数值例子说明了所得结果。
英文摘要
In this paper, we study sampled-data stabilization of general nonlinear stochastic systems under a local exponential-type Lyapunov condition for the continuous-time closed-loop system. The coefficients are assumed only locally Lipschitz, with neither linear-growth nor Khasminskii-type conditions. Two counterexamples show that almost-sure stabilization is generally unattainable. Instead, given an initial state, we establish exponential stability with arbitrarily high probability under sufficiently fast sampling. Separate methods are developed for \(p\ge 2\) and \(0<p<2\), where \(p\) is the growth order in the Lyapunov condition. Numerical examples illustrate the results.
