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

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.