On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term

2007 ◽  
Vol 56 (6) ◽  
pp. 423-430 ◽  
Author(s):  
Alexandra Rodkina ◽  
Michael Basin
Keyword(s):  
Difference Equations ◽  
Diffusion Term ◽  
Stochastic Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Delay Difference Equations ◽  
Delay Difference

scholarly journals Stability and Stabilization of Impulsive Stochastic Delay Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Kaining Wu ◽  
Xiaohua Ding ◽  
Liming Wang
Keyword(s):  
Difference Equations ◽  
Impulsive Control ◽  
Original System ◽  
Delay Difference Equation ◽  
Stochastic Delay ◽  
Razumikhin Technique ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Difference Equations ◽  
Delay Difference

When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable? If the SDDS is unstable, then what kind of impulsive strategy should be taken to make the system stable? Using the Lyapunov-Razumikhin technique, we establish criteria for the stability of impulsive stochastic delay difference equations and these criteria answer those questions. As for applications, we consider a kind of impulsive stochastic delay difference equation and present some corollaries to our main results.

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