具概率延迟反馈金融系统的脉冲控制  

Impulse Control of Financial Systems With Probabilistic Delay Feedback

作　　者：阿子阿英 饶若峰 赵锋[1] 黄鸿燕 王雪 刘浩 AZI Aying;RAO Ruofeng;ZHAO Feng;HUANG Hongyan;WANG Xue;LIU Hao(Department of Mathematics,Chengdu Normal University,Chengdu 611130,P.R.China;Institute of Financial Mathematics,Chengdu Normal University,Chengdu 611130,P.R.China)

机构地区：[1]成都师范学院数学学院,成都611130 [2]成都师范学院金融数字研究所,成都611130

出　　处：《应用数学和力学》2019年第12期1409-1416,共8页Applied Mathematics and Mechanics

基　　金：成都师范学院2018年国家级大学生创新创业训练计划项目(201814389083);成都师范学院2019年国家级大学生创新创业训练计划项目(201914389037)对本文的资助

摘　　要：研究了概率时滞脉冲金融系统平衡点的全局渐近稳定性问题.首先,通过定义合适的时滞分段区间上的随机变量,给出了概率时滞的脉冲金融系统的数学模型,根据脉冲微分不等式特点构造了一个简便合适的Lyapunov函数,利用脉冲微分不等式引理、控制脉冲间隔与脉冲量以及概率时滞分析技巧,获得了较大时滞允许范畴下的平衡点的全局指数稳定,并通过数值实例验证了方法的可行性以及概率时滞的优势.特别地,稳定性判定准则的时滞允许上限的增大,扩大了准则的实用性.The global asymptotic stability of equilibrium points of impulsive financial systems with probabilistic delays was studied.Firstly,through definition of the random variables on the appropriate time-delay intervals,the mathematical model for the impulsive financial system with probabilistic time delay was given.According to the characteristics of impulsive differential inequalities,a simple and suitable Lyapunov function was constructed.By means of the impulsive differential inequality lemma,the technique of controlling impulse interval&impulse quantity and the probabilistic time delay analysis,the global exponential stability of the equilibrium point in the permissible category of large delays was obtained.Finally,the feasibility of the proposed method and the advantages of probabilistic delay were verified with a numerical example.In particular,the increase of the time delay allowable upper limit to the stability criterion enlarges the practicability of the criterion.

关 键 词：概率时滞 脉冲微分不等式 LYAPUNOV函数 MATLAB LMI工具箱 

分 类 号：O175.13[理学—数学]