Stability and Stabilization of Impulsive Stochastic Delay Difference Equations
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/592036 |
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| _version_ | 1849305469081878528 |
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| author | Kaining Wu Xiaohua Ding Liming Wang |
| author_facet | Kaining Wu Xiaohua Ding Liming Wang |
| author_sort | Kaining Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0a2791d20c4d4b9e9f0d21ed718b024d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0a2791d20c4d4b9e9f0d21ed718b024d2025-08-20T03:55:27ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/592036592036Stability and Stabilization of Impulsive Stochastic Delay Difference EquationsKaining Wu0Xiaohua Ding1Liming Wang2Department of Mathematics, Harbin Institute of Technology, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology, Weihai 264209, ChinaWhen 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.http://dx.doi.org/10.1155/2010/592036 |
| spellingShingle | Kaining Wu Xiaohua Ding Liming Wang Stability and Stabilization of Impulsive Stochastic Delay Difference Equations Discrete Dynamics in Nature and Society |
| title | Stability and Stabilization of Impulsive Stochastic Delay Difference Equations |
| title_full | Stability and Stabilization of Impulsive Stochastic Delay Difference Equations |
| title_fullStr | Stability and Stabilization of Impulsive Stochastic Delay Difference Equations |
| title_full_unstemmed | Stability and Stabilization of Impulsive Stochastic Delay Difference Equations |
| title_short | Stability and Stabilization of Impulsive Stochastic Delay Difference Equations |
| title_sort | stability and stabilization of impulsive stochastic delay difference equations |
| url | http://dx.doi.org/10.1155/2010/592036 |
| work_keys_str_mv | AT kainingwu stabilityandstabilizationofimpulsivestochasticdelaydifferenceequations AT xiaohuading stabilityandstabilizationofimpulsivestochasticdelaydifferenceequations AT limingwang stabilityandstabilizationofimpulsivestochasticdelaydifferenceequations |