Some criteria on pth moment boundedness of impulsive stochastic functional differential equations
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- 英文论文题名：Some criteria on pth moment boundedness of impulsive stochastic functional differential equations
- 论文作者：Shiguo Peng ; Yunjian Xu
- 英文论文作者：Shiguo Peng ; Yunjian Xu ; School of Automation ; Guangdong University of Technology
- 年：2017
- 作者机构：School of Automation,Guangdong University of Technology;
- 英文论文关键词：Impulsive stochastic functional differential equations ; pth moment boundedness ; pth moment ultimate boundedness ; Razumikhin-type technique
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O211.63
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：240k
- 原文格式：D
- 会议级别：全国
摘要
This paper gives some Razumikhin-type theorems on pth moment boundedness of impulsive stochastic functional differential equations(ISFDEs) by using Razumikhin tenique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying(ISFDEs) of the Lyapunov function to have time-varying coefficients(the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results.
This paper gives some Razumikhin-type theorems on pth moment boundedness of impulsive stochastic functional differential equations(ISFDEs) by using Razumikhin tenique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying(ISFDEs) of the Lyapunov function to have time-varying coefficients(the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results.
This paper gives some Razumikhin-type theorems on pth moment boundedness of impulsive stochastic functional differential equations(ISFDEs) by using Razumikhin tenique and comparison principle. Some improved conditions on pth moment stability are also proposed. The main results of this paper allow the estimated upper bound of the diffusion operator associated with the underlying(ISFDEs) of the Lyapunov function to have time-varying coefficients(the coefficients may even be sign-changing functions). Examples are provided to illustrate the effectiveness of the proposed results.
引文
[1]X.Mao,Stochastic Differential Equations and Applications,2nd.Horwood Publishing,Chichester,2007.
[2]X.Mao,C.Yuan,Stochastic Differential Equations with Markovian Switching,Imperial College Press,London,2006.
[3]M.Basina,A.Rodkina,On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays,Nonlinear Analysis,68:2147-2157,2008.
[4]L.Huang,F.Deng,Razumikhin-type theorems on stability of neutral stochastic functional differential equations,IEEE Trans.Automat.Control,53:1718-1723,2008.
[5]L.Huang,X.Mao,On input-to-state of stochastic retarded systems with markovian switching,IEEE Trans.Automat.Control,54:1898-1902,2009.
[6]L.Huang,X.Mao,F.Deng,Stability of hybrid stochastic retarded system,IEEE Trans.Circ.Syst.I:Regular Papers,55:3413-3420,2008.
[7]Jankovi,S.,Randjelovi,J.,Jovanovi,M.,Razumikhintype exponential stability criteria of neutral stochastic functional differential equations,J.Math.Anal.Appl.,355:811-820,2009.
[8]X.Mao,J.Lam,S.Xu,H.Gao,Razumikhin method and exponential stability of hybrid stochastic delay interval systems,J.Math.Anal.Appl.314:45-66,2006.
[9]J.Randjelovi,S.Jankovi,On the pth moment exponential stability criteria of neutral stochastic functional differential equations,J.Math.Anal.Appl.,326:266-280,2007.
[10]X.Mao,Attraction,stability and boundedness for stochastic differential delay equations.Nonlinear Anal.,47:4795-4806,2001.
[11]Q.Luo,X.Mao,Y.Shen,Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations,Automatica,47:2075-2081,2011.
[12]J.Liu,On asymptotic convergence and boundedness of stochastic systems with time-delay,Automatica,48:3166-3172,2012.
[13]L.Wan,Q.H.Zhou,P.Wang,J.Li,Ultimate boundedness and an attractor for stochastic Hopfield neural networks with time-varying delays,Nonlinear Analysis:Real World Appl.,13:953-958,2012.
[14]Z.Yang,D.Xu,L.Xiang,Exponential p-stability of impulsive stochastic differential equations with delays,Phys.Lett.A,359:129-137,2006.
[15]L.Xu,D.Xu,Mean square exponential stability of impulsive control stochastic systems with-varying delay,Phys.Lett.A,373:328-333,2009.
[16]Q.Song,Z.Wang,Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,Physica A,387:3314-3326,2008.
[17]X.Wang,Q.Guo,D.Xu,Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,Mathematics and Computers in Simulation,79:1698-1170,2009.
[18]J.Yang,S.Zhong,W.Luo,Mean square stability analysis of impulsive stochastic differential equations with delays,J.Comput.Appl.Math.,216:474-483,2008.
[19]S.Peng,Y.Zhang,Razumikhin-type theorems on pth moment exponential stability of impulsive stochastic delay differential equations,IEEE Trans.Automat.Control,55:1917-1922,2010.
[20]J.Liu,X.Liu,W.Xie,Impulsive stabilization of stochastic functional differential equations,Appl.Math.Lett.,24:264-269,2011.
[21]L.Pan,J.Cao,Exponential stability of impulsive stochastic functional differential equations,J.Math.Anal.Appl.,382:672-685,2011.
[22]P.Cheng,F.Deng,Q.Yao,Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses,Commun.Nonlinear Sci.Numer.Simulat.,19:2104-2114,2014.
[23]X.Li,Q.Zhu,D.O’Regan,pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs,J.Franklin Inst.351:4435-4456,2014.
[24]S.Peng,B.Jia,Some criteria on pth moment stability of impulsive stochastic functional differential equations,Statistics&Probatlity Letters,80:1085-1092,2010.
[25]L.Wang,B.Yang,X.Ding,K.Wu,Boundedness of stochastic delay differential systems with impulsive control and impulsive disturbance,Mathematical Problems in Engineering,Volume 2015,Article ID 707069,2015.
[26]L.Xu,S.Ge,The pth moment exponential utimate boundedness of impulsive stochastic differential systems,Appl.Math.Lett.,43:22-29,2015.
[27]M.Alwan,X.Liu,W.Xie,Existence,continuation,and uniqueness problems of stochastic impulsive systems with time delay,J.Franklin Inst.,347:1317-1333,2010.
[2]X.Mao,C.Yuan,Stochastic Differential Equations with Markovian Switching,Imperial College Press,London,2006.
[3]M.Basina,A.Rodkina,On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays,Nonlinear Analysis,68:2147-2157,2008.
[4]L.Huang,F.Deng,Razumikhin-type theorems on stability of neutral stochastic functional differential equations,IEEE Trans.Automat.Control,53:1718-1723,2008.
[5]L.Huang,X.Mao,On input-to-state of stochastic retarded systems with markovian switching,IEEE Trans.Automat.Control,54:1898-1902,2009.
[6]L.Huang,X.Mao,F.Deng,Stability of hybrid stochastic retarded system,IEEE Trans.Circ.Syst.I:Regular Papers,55:3413-3420,2008.
[7]Jankovi,S.,Randjelovi,J.,Jovanovi,M.,Razumikhintype exponential stability criteria of neutral stochastic functional differential equations,J.Math.Anal.Appl.,355:811-820,2009.
[8]X.Mao,J.Lam,S.Xu,H.Gao,Razumikhin method and exponential stability of hybrid stochastic delay interval systems,J.Math.Anal.Appl.314:45-66,2006.
[9]J.Randjelovi,S.Jankovi,On the pth moment exponential stability criteria of neutral stochastic functional differential equations,J.Math.Anal.Appl.,326:266-280,2007.
[10]X.Mao,Attraction,stability and boundedness for stochastic differential delay equations.Nonlinear Anal.,47:4795-4806,2001.
[11]Q.Luo,X.Mao,Y.Shen,Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations,Automatica,47:2075-2081,2011.
[12]J.Liu,On asymptotic convergence and boundedness of stochastic systems with time-delay,Automatica,48:3166-3172,2012.
[13]L.Wan,Q.H.Zhou,P.Wang,J.Li,Ultimate boundedness and an attractor for stochastic Hopfield neural networks with time-varying delays,Nonlinear Analysis:Real World Appl.,13:953-958,2012.
[14]Z.Yang,D.Xu,L.Xiang,Exponential p-stability of impulsive stochastic differential equations with delays,Phys.Lett.A,359:129-137,2006.
[15]L.Xu,D.Xu,Mean square exponential stability of impulsive control stochastic systems with-varying delay,Phys.Lett.A,373:328-333,2009.
[16]Q.Song,Z.Wang,Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays,Physica A,387:3314-3326,2008.
[17]X.Wang,Q.Guo,D.Xu,Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,Mathematics and Computers in Simulation,79:1698-1170,2009.
[18]J.Yang,S.Zhong,W.Luo,Mean square stability analysis of impulsive stochastic differential equations with delays,J.Comput.Appl.Math.,216:474-483,2008.
[19]S.Peng,Y.Zhang,Razumikhin-type theorems on pth moment exponential stability of impulsive stochastic delay differential equations,IEEE Trans.Automat.Control,55:1917-1922,2010.
[20]J.Liu,X.Liu,W.Xie,Impulsive stabilization of stochastic functional differential equations,Appl.Math.Lett.,24:264-269,2011.
[21]L.Pan,J.Cao,Exponential stability of impulsive stochastic functional differential equations,J.Math.Anal.Appl.,382:672-685,2011.
[22]P.Cheng,F.Deng,Q.Yao,Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses,Commun.Nonlinear Sci.Numer.Simulat.,19:2104-2114,2014.
[23]X.Li,Q.Zhu,D.O’Regan,pth Moment exponential stability of impulsive stochastic functional differential equations and application to control problems of NNs,J.Franklin Inst.351:4435-4456,2014.
[24]S.Peng,B.Jia,Some criteria on pth moment stability of impulsive stochastic functional differential equations,Statistics&Probatlity Letters,80:1085-1092,2010.
[25]L.Wang,B.Yang,X.Ding,K.Wu,Boundedness of stochastic delay differential systems with impulsive control and impulsive disturbance,Mathematical Problems in Engineering,Volume 2015,Article ID 707069,2015.
[26]L.Xu,S.Ge,The pth moment exponential utimate boundedness of impulsive stochastic differential systems,Appl.Math.Lett.,43:22-29,2015.
[27]M.Alwan,X.Liu,W.Xie,Existence,continuation,and uniqueness problems of stochastic impulsive systems with time delay,J.Franklin Inst.,347:1317-1333,2010.