Exponential Stability of Impulsive Stochastic Delay Differential Systems | Zendy

Xiaotai Wu | Zendy; Litan Yan | Zendy; Wenbing Zhang | Zendy; Liang Chen | Zendy

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Exponential Stability of Impulsive Stochastic Delay Differential Systems

Author(s) -

Xiaotai Wu,

Litan Yan,

Wenbing Zhang,

Liang Chen

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/296136

Subject(s) - interval (graph theory) , stability (learning theory) , upper and lower bounds , exponential stability , exponential function , mathematics , moment (physics) , impulse (physics) , differential equation , stochastic differential equation , computer science , control theory (sociology) , mathematical analysis , physics , combinatorics , artificial intelligence , control (management) , classical mechanics , nonlinear system , machine learning , quantum mechanics

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the pth moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples

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