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

2022/07/24 by Zhang, Weihai, Yao, Liqiang
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2207.11642

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 LV (the infinitesimal operator of Lyapunov function V) by the uniformly asymptotically stable function(UASF). The improved finite-time stability theorems allow \mathcal LV to be indefinite (negative or positive) rather than just only allow \mathcal LV 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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