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Liu, Jun; Liu, Xinzhi; Xie, Wei-Chau

Impulsive stabilization of stochastic functional differential equations. (English) Zbl 1209.34097

Appl. Math. Lett. 24, No. 3, 264-269 (2011).
Summary: This paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov-Razumikhin method. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An example with its numerical simulation is presented to illustrate the main results.

Cited in 28 Documents

MSC:

34K45 Functional-differential equations with impulses
34K50 Stochastic functional-differential equations
34K20 Stability theory of functional-differential equations

Keywords:

impulsive control; impulsive stabilization; stochastic delay differential equation; Lyapunov exponent; exponential stability; Lyapunov-Razumikhin method
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\textit{J. Liu} et al., Appl. Math. Lett. 24, No. 3, 264--269 (2011; Zbl 1209.34097)
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