论文标题
随机非线性系统的有限时间稳定性和不稳定性定理
Improved finite-time stability and instability theorems for stochastic nonlinear systems
论文作者
论文摘要
本文研究了随机非线性系统的概率意义上的有限时间稳定性和不稳定性定理。首先，提出了一种新的足够条件，以确保所考虑的系统具有全球解决方案。其次，我们提出了改进的有限时间稳定性和不稳定性标准，以放大均匀渐近稳定函数（UASF）的$ \ Mathcal {L} V $（Lyapunov函数$ V $的无限运算符）的约束。改进的有限时间稳定性定理允许$ \ mathcal {l} v $不确定（负或正），而不仅仅是允许$ \ Mathcal {l} v $为负。大多数现有的有限时间稳定性和不稳定性结果可以看作是所获得定理的特殊情况。最后，一些模拟示例验证了理论结果的有效性。
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution. Secondly, we propose improved finite-time stability and instability criteria that relax the constraints on $\mathcal {L}V$ (the infinitesimal operator of Lyapunov function $V$) by the uniformly asymptotically stable function(UASF). The improved finite-time stability theorems allow $\mathcal {L}V$ to be indefinite (negative or positive) rather than just only allow $\mathcal {L}V$ to be negative. Most existing finite-time stability and instability results can be viewed as special cases of the obtained theorems. Finally, some simulation examples verify the validity of the theoretical results.
