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arXiv · 2207.11642

Improved finite-time stability and instability theorems for stochastic nonlinear systems

Weihai Zhang·Liqiang Yao
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Abstract

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.

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Weihai Zhang, Liqiang Yao. 2022-07-24. Improved finite-time stability and instability theorems for stochastic nonlinear systems. https://arxiv.org/abs/2207.11642

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