Stabilization in Distribution of Hybrid Systems by Intermittent Noise

主讲人：胡军浩 中南民族大学教授

时间：2023年5月17日16：30

地点：三号楼332

举办单位：数理学院

主讲人介绍：胡军浩, 男，博士, 博士后经历，教授，硕士生导师，中南民族大学数学与统计学学院院长。2007年毕业于华中科技大学，获理学博士学位。2008年至2010年, 在华中科技大学从事博士后研究。 2011年至2012年, 在英国Strathclyde大学和Swansea大学从事博士后研究。2014年被中南民族大学聘为教授。主要研究领域为随机系统理论与应用，动力系统。主持国家自然科学基金面上项目、国家自然科学基金青年项目、湖北省自然科学基金、国家博士后基金和中南民族大学校科研项目等，参加国家自然科学基金重点项目。已在国内外学术期刊上发表论文50余篇。获得湖北省自然科学奖（三等奖）。

内容介绍：For many stochastic hybrid systems in the real world, it is inappropriate to study if their solutions will converge to an equilibrium state (say, 0 by default) but more appropriate to discuss if the probability distributions of the solutions will converge to a stationary distribution. The former is known as the asymptotic stability of the equilibrium state while the latter the stability in distribution. This paper aims to determine whether or not a stochastic state feedback control can make a given non- linear hybrid differential equation, which is not stable in distribution, to become stable in distribution. We will refer to this problem as stabilisation in distribution by noise or stochastic stabilisation in distribution. Although the stabilisation by noise in the sense of almost surely exponential stability of the equilibrium state has been well studied, there is little known on the stabilisation in distribution by noise. This paper initiates the study in this direction.