报告人：朱全新   湖南师范大学 数学与统计学院

时间：2020年11月25日（星期三）晚上19：00-21：50

地点：002cc白菜资讯三楼会议室

报告人简介：

朱全新，博士，湖南师范大学潇湘学者特聘教授, 博士生导师, 湖南省芙蓉学者特聘教授、德国洪堡基金高访学者，计算与随机数学教育部重点实验室副主任，IEEE高级会员。主要从事马氏过程、随机系统的稳定与控制理论及应用研究工作, 取得了系列重要进展, 解决了SIAM J. Control Optim.等国际权威刊物上提出的多个公开问题。在控制理论国际顶级刊物Automatica、IEEE Transactions on Automatic Control等杂志发表SCI收录论文150篇,论文被SCI他引3000多次。发表在《Nonlinear Anal.: RWA》的SCI文章被评为2012年度Science Direct数据库中最热门的25篇文章之一。获2018和2019连续两年全球高被引科学家、2018年国家教学成果奖二等奖、2016年江苏省“高校自然科学奖”一等奖、2014-2019连续六年爱思唯尔中国高被引学者榜单、2017年江苏省 “教学成果奖”一等奖、2019年湖南省芙蓉学者特聘教授. 2019年湖湘高层次人才聚集工程-创新人才项目、2017年江苏省“六大人才高峰”高层次项目、2016年江苏省“青蓝工程”中青年学科带头人培养对象、2015年南京市政府突出贡献中青年专家、2014年第四届江苏省数学成就奖、2011年度“中国百篇最具国际影响”学术论文、2008年第三届中国运筹学会“青年科技奖”二等奖等。主持国际项目2项，国家自然科学基金项目4项，省部级项目8项，省教育厅重点项目1项，作为第二参与人承担国家自然科学基金重点项目1项，担任8个国际刊物的编委，4个国际刊物特刊的客座主编或编辑。

报告题目（一）: Stability analysis of stochastic differential equations driven by Levy processes

摘要: In this talk, we first introduce the background, definition and properties of Levy processes, and then present stochastic differential equations driven by Levy processes. In comparison to the standard Gaussian noise, Levy noise has more versatile and interesting with a wider range of applications. However, Levy noise makes the analysis more difficult owing to the discontinuity of its sample paths. We attempt to overcome this difficulty and discuss the existence and uniqueness of the solution as well as several stochastic stability criteria, etc. Furthermore, we consider the exponential stability problem for a class of stochastic delay differential equations driven by Levy processes. Several new stability theorems are obtained by developing a method-----proof by contradiction. In particular, the time-varying delay in our results is not required to be differentiable, even not continuous. Our results improve greatly some previous works given in the literature.

报告题目（二）: Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion

摘要: In this talk, we discuss the pth moment exponential stability problem for a class of stochastic delay nonlinear systems (SDNSs) driven by G-Brownian motion. The delays considered here are time-varying delaysand they are not required to be differentiable. Different from the traditional methods, we use a new approach: stochastic delay feedback controls. We firstly compare the SDNS with the corresponding stochastic nonlinear system (SNS) instead of studying the stability of the SDNS directly. Then, we impose the condition on the SNS to ensure the pth moment exponential stability of the SNS. Furthermore, we show that there is a positive constant τ∗ such that the SDNS is also pth moment exponentially stable provided τ<τ∗. In particular, we give an implicit lower bound for τ∗ which can be computed numerically.

报告题目（三）: Stability analysis of impulsive stochastic delayed differential systems with unbounded delays

摘要: In this talk, we discuss the stability analysis for impulsive stochastic delayed differential equations with unbounded delays by applying stochastic analysis techniques and average dwell time approach. A novel Razumikhin-type criterion of the pth moment exponential stability is derived for the related systems. The feature of the criterion shows that time-derivatives of the Lyapunov functions are allowed to be indefinite, even unbounded, which can loosen the constraints of the existing results. As a corollary, the criterion of the pth moment exponential stability for stochastic delayed differential equations with unbounded delays without impulsive effects is also obtained. Finally, some examples are given to illustrate the usefulness and significance of the theoretical results.