Impulsive control of stochastic system under the sense of stochastic asymptotical stability

doi:10.1088/1674-1056/19/11/110511

中国物理B ›› 2010, Vol. 19 ›› Issue (11): 110511-110514.doi: 10.1088/1674-1056/19/11/110511

Impulsive control of stochastic system under the sense of stochastic asymptotical stability

牛玉俊, 马戈

Department of Applied Math, Nanyang Institute of Technology, Nanyang 473004, China

收稿日期:2009-09-25 修回日期:2010-05-07 出版日期:2010-11-15 发布日期:2010-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10902085).

Impulsive control of stochastic system under the sense of stochastic asymptotical stability

Niu Yu-Jun(牛玉俊)^† and Ma Ge(马戈)

Department of Applied Math, Nanyang Institute of Technology, Nanyang 473004, China

Received:2009-09-25 Revised:2010-05-07 Online:2010-11-15 Published:2010-11-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10902085).

摘要/Abstract

摘要： This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lü system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.

Abstract: This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lü system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.

Key words: stochastic impulsive system, stochastic asymptotical stability, comparison theory, impulsive control

中图分类号: (Ordinary differential equations)

02.30.Hq

02.50.Ey (Stochastic processes) 05.45.Pq (Numerical simulations of chaotic systems)

牛玉俊, 马戈. Impulsive control of stochastic system under the sense of stochastic asymptotical stability[J]. 中国物理B, 2010, 19(11): 110511-110514.

Niu Yu-Jun(牛玉俊) and Ma Ge(马戈). Impulsive control of stochastic system under the sense of stochastic asymptotical stability[J]. Chin. Phys. B, 2010, 19(11): 110511-110514.

参考文献 26

[1]	Hu M F, Yang Y Q and Xu Z Y 2008 wxPhys. Lett. A 372 3228
[2]	Lakshmikantham V, Bainov D D and Simeonov P S 1989 wxTheory of Impulsive Differential Equations (Singapore; World Scientific)
[3]	Yang T 2001 wxImpulsive Control Theory (Berlin: Springer)
[4]	Yang T, Yang L B and Yang C M 1997 wxPhys. Lett. A 226 349
[5]	Yang T, Yang L B and Yang C M 1997 wxPhys. D 110 18
[6]	Yang T, Yang L B and Yang C M 1997 wxPhys. Lett. A 232 356
[7]	Soliman A A 2002 wxAppl. Math. Comput. 133 105
[8]	Panas A I , Yang T and Chua L O 1998 wxInt. J. Bifur. Chaos 3 639
[9]	Jiao J J, Chen L S and Li L M 2008 wxMath. Anal. Appl. 337 458
[10]	Chen L L, Sun J T and Wu Q D 2004 wxChaos, Solitons and Fractals 21 135
[11]	Mohamad S and Gopalsamy K 2009 wxCommun. Nonlinear. Sci. Numer. Simulat. 14 27
[12]	Li K and Lai C H 2008 wxPhys. Lett. A 372 1601
[13]	Liu X W, Huang Q Z, Gao X and Shao S Q 2007 wxChin. Phys. 16 2272
[14]	Zhang H G, Fu J, Ma T D and Tong S C 2009 wxChin. Phys. B 18 969
[15]	Li Y, Liao X F, Li C D and Chen G 2006 wxChin. Phys. 15 2890
[16]	Wu S J, Han D and Meng X Z 2004 wxAppl. Math. Comput. 152 505
[17]	Yang Z G, Xu D Y and Li X 2006 wxPhys. Lett. A 359 129
[18]	Yang J, Zhong S M and Luo W P 2009 wxJ. Comput. Appl. Math. 216 474
[19]	Dong Y W and Sun J T 2005 wxChaos, Solitons and Fractals 26 1491
[20]	Zhang H, Guan Z H and Feng G 2008 wxAutomatica 44 1004
[21]	Wang Q K and Song Z D 2008 wxPhys. A387 3314
[22]	Li C G, Chen L N and Kazuyuki A 2008 wxChaos 18 023132.
[23]	Niu Y J, Xu W, Rong H W, Wang L and Feng J Q 2009 wxActa Phys. Sin. 58 2983 (in Chinese)
[24]	Niu Y J, Xu W and Lu Z Y 2010 wxChin. Phys. B 19 030512
[25]	Hu X D and Yu Z M 1980 wxJ. Nanjing University 3 1
[26]	Hu X D and Yu Z M 1982 wxActa. Math. Sin. 25 427 endfootnotesize

Impulsive control of stochastic system under the sense of stochastic asymptotical stability

Impulsive control of stochastic system under the sense of stochastic asymptotical stability

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