New results on finite-time stability and instability theorems for stochastic nonlinear time-varying systems  

作　　者：Weihai ZHANG Liqiang YAO 

机构地区：[1]College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266590,China [2]School of Mathematics and Information Science,Yantai University,Yantai 264005,China

出　　处：《Science China(Information Sciences)》2025年第2期182-195,共14页中国科学(信息科学)(英文版)

基　　金：supported by National Natural Science Foundation of China(Grant No.62373229);Shandong Provincial Natural Science Foundation of China(Grant No.ZR2020MA033);Research Fund for the Taishan Scholar Project of Shandong Province of China。

摘　　要：This paper studies finite-time stability and instability theorems in the probability sense for stochastic nonlinear timevarying systems.Firstly,a new sufficient condition is proposed to guarantee that the considered system has a global solution.Secondly,we propose new finite-time stability and instability criteria that relax the constraints on LV(the infinitesimal operator of Lyapunov function V)by the uniformly asymptotically stable function.On the one hand,these obtained results make up for the shortcomings of the existing results.On the other hand,the new finite-time stability theorems can be viewed as natural extensions of the existing results and also allow LV to be indefinite(negative or positive)rather than just only allow LV<0.Finally,some simulation examples verify the validity of the theoretical results.

关 键 词：stochastic nonlinear systems finite-time stability finite-time instability uniformly asymptotically stable function 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]