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**Exponential stability of impulsive stochastic functional differential systems with delayed impulses.**
*(English)*
Zbl 1271.93169

Summary: A class of generalized impulsive stochastic functional differential systems with delayed impulses is considered. By employing piecewise continuous Lyapunov functions and the Razumikhin techniques, several criteria on the exponential stability and uniform stability in terms of two measures for the mentioned systems are obtained, which show that unstable stochastic functional differential systems may be stabilized by appropriate delayed impulses. Based on the stability results, delayed impulsive controllers which mean square exponentially stabilize linear stochastic delay systems are proposed. Finally, numerical examples are given to verify the effectiveness and advantages of our results.

### MSC:

93E15 | Stochastic stability in control theory |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

93D30 | Lyapunov and storage functions |

### Keywords:

generalized impulsive stochastic functional differential systems; piecewise continuous Lyapunov functions; Razumikhin techniques; exponential stability; uniform stability
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\textit{F. Yao} et al., Abstr. Appl. Anal. 2013, Article ID 548712, 8 p. (2013; Zbl 1271.93169)

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### References:

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