Stability analysis of nonlinear stochastic differential delay systems under impulsive control

In this Letter, we study the stability of nonlinear stochastic differential delay systems under impulsive control. First, we construct an impulsive control for a nonlinear stochastic differential delay system. Then, the equivalent relation between the stability of the nonlinear stochastic differential delay system under impulsive control and that of a corresponding nonlinear stochastic differential delay system without impulses is established. Third, some sufficient conditions ensuring various stabilities of the nonlinear stochastic differential delay systems under impulsive control are obtained. Finally, an example is also discussed to illustrate the effectiveness of the obtained results.

[1]  Hai-Feng Huo,et al.  Existence and global attractivity of positive periodic solutions of functional differential equations with impulses , 2004 .

[2]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[3]  Shouming Zhong,et al.  Mean square stability analysis of impulsive stochastic differential equations with delays , 2008 .

[4]  J. Nieto,et al.  New results for the periodic boundary value problem for impulsive integro-differential equations , 2009 .

[5]  Katrin Rohlf,et al.  Impulsive control of a Lotka-Volterra system , 1998 .

[6]  X. Mao,et al.  Stability and stabilisation of stochastic differential delay equations , 2007 .

[7]  Xuerong Mao,et al.  Stochastic delay Lotka-Volterra model , 2004 .

[8]  J. Ruan,et al.  Global stability analysis of impulsive Cohen–Grossberg neural networks with delay , 2005 .

[9]  Zidong Wang,et al.  Robust stability of discrete-time stochastic neural networks with time-varying delays , 2008, Neurocomputing.

[10]  Jiaowan Luo.  A note on exponential stability in p th mean of solutions of stochastic delay differential equations , 2007 .

[11]  Zhiguo Yang,et al.  Exponential p-stability of impulsive stochastic differential equations with delays , 2006 .

[12]  John E. Prussing,et al.  Optimal Impulsive Time-Fixed Direct-Ascent Interception , 1989 .

[13]  Zheng-Guang Wu,et al.  Improved result on stability analysis of discrete stochastic neural networks with time delay , 2009 .

[14]  Qidi Wu,et al.  Impulsive robust control of uncertain Luré systems , 2002 .

[15]  Wei Ding.  Synchronization of delayed fuzzy cellular neural networks with impulsive effects , 2009 .

[16]  Jitao Sun,et al.  Stability of linear stochastic differential delay systems under impulsive control , 2009 .

[17]  Pagavathigounder Balasubramaniam,et al.  Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays , 2008 .

[18]  Maoan Han,et al.  Exponential lag synchronization of delayed fuzzy cellular neural networks with impulses , 2009 .

[19]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[20]  Zhiguo Luo,et al.  Stability of impulsive functional differential equations via the Liapunov functional , 2009, Appl. Math. Lett..

[21]  Zhi-Hong Guan,et al.  Stability analysis on uncertain stochastic impulsive systems with time-delay , 2008 .

[22]  Yu Zhang,et al.  Stability of impulsive functional differential equations , 2008 .

[23]  Jianhua Shen.  Razumikhin techniques in impulsive functional differential equations , 1999 .

[24]  R. Sakthivel,et al.  Asymptotic stability of impulsive stochastic partial differential equations with infinite delays , 2009 .