AZI Aying, RAO Ruofeng, ZHAO Feng, HUANG Hongyan, WANG Xue, LIU Hao. Impulse Control of Financial Systems With Probabilistic Delay Feedback[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1409-1416. doi: 10.21656/1000-0887.400059
 Citation: AZI Aying, RAO Ruofeng, ZHAO Feng, HUANG Hongyan, WANG Xue, LIU Hao. Impulse Control of Financial Systems With Probabilistic Delay Feedback[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1409-1416.

# Impulse Control of Financial Systems With Probabilistic Delay Feedback

##### doi: 10.21656/1000-0887.400059
• Rev Recd Date: 2019-02-28
• Publish Date: 2019-12-01
• 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.
•  [1] 马军海, 陈予恕. 一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究[J]. 应用数学和力学, 2001,22(11): 1119-1128.(MA Junhai, CHEN Yushu. Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system[J]. Applied Mathematics and Mechanics,2001,22(11): 1119-1128.(in Chinese)) [2] 马军海, 陈予恕. 一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究[J]. 应用数学和力学, 2001,22(12): 1236-1242.(MA Junhai, CHEN Yushu. Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system[J]. Applied Mathematics and Mechanics,2001,22(12): 1236-1242.(in Chinese)) [3] ZHANG R Y. Bifurcation analysis for a kind of nonlinear finance system with delayed feedback and its application to control of chaos[J]. Journal of Applied Mathematics,2012,2012: 316390. [4] PYRAGAS K. Continuous control of chaos by self-controlling feedback[J]. Physics Letters A,1992,170(6): 421-429. [5] CHEN W C. Dynamics and control of a financial system with time-delayed feedbacks[J]. Chaos, Solitons & Fractals,2008,37(4): 1198-1207. [6] 姚洪兴, 潘虹, 齐丽丽. 一类含脉冲延迟反馈金融系统的稳定性分析[J]. 江苏大学学报(自然科学版), 2011,〖STHZ〗 32(2): 241-244.(YAO Hongxing, PAN Hong, QI Lili. Global exponential stability of a financial system with impulses and time-delayed feedbacks[J]. Journal of Jiangsu University(Science Edition),2011,32(2): 241-244.(in Chinese)) [7] RAO R F, ZHONG S M, WANG X R. Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with p -Laplace diffusion and partially known transition rates via a differential inequality[J]. Advances in Difference Equations,2013,2013: 183. [8] SONG Q K, YAN H, ZHAO Z J, et al. Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays[J]. Neural Networks,2016,81: 1-10. [9] WANG L M, SONG Q K, LIU Y R, et al. Global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay[J]. Neurocomputing,2017,243: 49-59. [10] 岳东, 许世范, 刘永清. 脉冲时滞微分不等式及鲁棒控制设计中的应用[J]. 控制理论与应用, 1999,16(4): 519-524.(YUE Dong, XU Shifan, LIU Yongqing. Differential inequality with delay and impulse and its applications to design robust control[J]. Control Theory Applications,1999,16(4): 519-524.(in Chinese)) [11] 张磊, 宋乾坤. 带有比例时滞的复值神经网络全局指数稳定性[J]. 应用数学和力学, 2018,39(5): 584-591.(ZHANG Lei, SONG Qiankun. Global exponential stability of complex-valued neural networks with proportional delays[J]. Applied Mathematics and Mechanics,2018,39(5): 584-591.(in Chinese)) [12] 舒含奇, 宋乾坤. 带有时滞的Clifford值神经网络的全局指数稳定性[J]. 应用数学和力学, 2017,38(5): 513-525.(SHU Hanqi, SONG Qiankun. Global stability of Clifford-valued recurrent neural networks with mixed time-varying delays[J]. Applied Mathematics and Mechanics,2017,38(5): 513-525.(in Chinese)) [13] ZHANG X H, WU S L, LI K L. Delay-dependent exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms[J]. Communications in Nonlinear Science and Numerical Simulation,2011,16(3): 1524-1532. [14] 黎克麟, 曾意. 具有多滞后的区间非线性Lurie控制系统的鲁棒绝对稳定性[J]. 四川师范大学学报(自然科学版), 2007,30(1): 27-30.(LI Kelin, ZENG Yi. Robust absolute stability of interval nonlinear Lurie control systems with multi-delay[J]. Journal of Sichuan Normal University（Natural Scicence）,2007,30(1): 27-30.(in Chinese)) [15] LI K L, ZHANG X H, LI Z A. Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay[J]. Chaos, Solitons & Fractals,2009,41(3): 1427-1434. [16] 曾德强, 吴开腾, 宋乾坤, 等. 时滞神经网络随机抽样控制的状态估计[J]. 应用数学和力学, 2018,39(7): 821-832.(ZENG Deqiang, WU Kaiteng, SONG Qiankun, et al. State estimation for delayed neural networks with stochastic sampled-data control[J]. Applied Mathematics and Mechanics,2018,39(7): 821-832.(in Chinese)) [17] RAO Ruofeng. Global stability of a Markovian jumping chaotic financial system with partially unknown transition rates under impulsive control involved in the positive interest rate[J]. Mathematics,2019,7(7): 579.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142