On partial stability in probability for nonlinear stochastic functional differential systems with aftereffect (delay)

Author:

Vorotnikov V. I.1,Martyshenko Yu. G.2

Affiliation:

1. RUDN University, Sochi Institute

2. Gubkin University Oil and Gas

Abstract

A system of nonlinear functional-differential equations with aftereffect (delay) subjected to random processes of “white” noise is considered. It is assumed that the system admits a “partial” (with respect to some part of the state variables) zero equilibrium position. The problem of stability in probability of a given equilibrium position is posed, and stability is considered not in all, but with respect to a part of the variables that determine this equilibrium position. For the solution of this problem, a stochastic version of the method of Lyapunov—Krasovskii functionals is used with the appropriated specification of the requirements for the functionals. In order to expend the capabilities of the method used, it is also proposed to correct the domain of the functional space in which auxiliary Lyapunov—Krasovskii functionals are constructed. Conditions for partial stability of this type are obtained. Examples are given that show the features of the proposed approach.

Publisher

The Russian Academy of Sciences

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3