华东师范大学学报（自然科学版） >

2023 , Vol. 2023 >Issue 4: 11 - 23

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.04.002

数学

一类由α-稳定过程驱动的随机时滞微分方程的LaSalle不变原理

  • 张振中 ,
  • 陈旭 ,
  • 童金英
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  • 东华大学 理学院, 上海　201620
张振中, 男, 教授, 研究方向为受控的混杂跳扩散系统及应用. E-mail: zzzhang@dhu.edu.cn

收稿日期: 2021-09-24

  网络出版日期: 2023-07-25

基金资助

国家自然科学基金 (12171081); 上海市自然科学基金 (22WZ2505700, 23ZR1402600); 东华大学虚拟仿真实验教学项目; 东华大学一流本科课程(DHYLA-2022-23); 东华大学偏微分方程示范教研室(SFJYS2021-05)

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LaSalle’s invariance principle for delay differential equations driven by α-stable processes

  • Zhenzhong ZHANG ,
  • Xu CHEN ,
  • Jinying TONG
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  • College of Science, Donghua University, Shanghai　201620, China

Received date: 2021-09-24

  Online published: 2023-07-25

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摘要

LaSalle 不变原理是研究随机系统稳定性的重要工具. 考虑到时滞与样本轨道跳跃对系统稳定性的影响, 本文通过特殊半鞅的收敛性, 建立了一类由 $\alpha$ -稳定过程驱动的随机时滞微分方程的 LaSalle 不变原理. 利用 LaSalle 不变原理给出了一类延迟方程解渐进稳定的充分条件.

关键词： LaSalle 不变原理; 特殊半鞅; 依概率渐近稳定性; 依概率稳定性

本文引用格式

张振中 , 陈旭 , 童金英 . 一类由α-稳定过程驱动的随机时滞微分方程的LaSalle不变原理[J]. 华东师范大学学报（自然科学版）, 2023 , 2023(4) : 11 -23 . DOI: 10.3969/j.issn.1000-5641.2023.04.002

Abstract

LaSalle’s invariance principle is an important tool for studying the stability of stochastic systems. Considering the influence of time delay and pure-jump path on the stability of the system and using the convergence theorem for special semi-martingale, the LaSalle’s invariance principle for a class of stochastic delay differential equations driven by $\alpha$ -stable processes is established in this study. The sufficient conditions for the asymptotic stability of a class of delay equations are given by LaSalle’s invariance principle.

Key words： LaSalle’s invariance principle; special semi-martingale; asymptotic stability in probability; stability in probability

参考文献

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