On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays
This paper is concerned with pth moment input-to-state stability (p-ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic systems with time delays. Razumikhin-type theorems ensuring p-ISS/SISS are established for the mentioned systems with external input affecting both the cont...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/589562 |
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| author | Fengqi Yao Pei Cheng Hao Shen Li Qiu |
| author_facet | Fengqi Yao Pei Cheng Hao Shen Li Qiu |
| author_sort | Fengqi Yao |
| collection | DOAJ |
| description | This paper is concerned with pth moment input-to-state stability (p-ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic systems with time delays. Razumikhin-type theorems ensuring p-ISS/SISS are established for the mentioned systems with external input affecting both the continuous and the discrete dynamics. It is shown that when the impulse-free delayed stochastic dynamics are p-ISS/SISS but the impulses are destabilizing, the p-ISS/SISS property of the impulsive stochastic systems can be preserved if the length of the impulsive interval is large enough. In particular, if the impulse-free delayed stochastic dynamics are p-ISS/SISS
and the discrete dynamics are marginally stable for the zero input, the impulsive stochastic system is p-ISS/SISS regardless of how often or how seldom the impulses occur. To overcome the difficulties caused by the coexistence of time delays, impulses, and stochastic effects, Razumikhin techniques and piecewise continuous Lyapunov functions as well as stochastic analysis techniques are involved together. An example is provided to illustrate the effectiveness and advantages of our results. |
| format | Article |
| id | doaj-art-6afe82b7b6b44e0cb8d04348fe2d39c9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6afe82b7b6b44e0cb8d04348fe2d39c92025-08-20T03:34:00ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/589562589562On Input-to-State Stability of Impulsive Stochastic Systems with Time DelaysFengqi Yao0Pei Cheng1Hao Shen2Li Qiu3School of Electrical Engineering & Information, Anhui University of Technology, Maanshan 243000, ChinaSchool of Mathematical Science, Anhui University, Hefei 230039, ChinaSchool of Electrical Engineering & Information, Anhui University of Technology, Maanshan 243000, ChinaCollege of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, ChinaThis paper is concerned with pth moment input-to-state stability (p-ISS) and stochastic input-to-state stability (SISS) of impulsive stochastic systems with time delays. Razumikhin-type theorems ensuring p-ISS/SISS are established for the mentioned systems with external input affecting both the continuous and the discrete dynamics. It is shown that when the impulse-free delayed stochastic dynamics are p-ISS/SISS but the impulses are destabilizing, the p-ISS/SISS property of the impulsive stochastic systems can be preserved if the length of the impulsive interval is large enough. In particular, if the impulse-free delayed stochastic dynamics are p-ISS/SISS and the discrete dynamics are marginally stable for the zero input, the impulsive stochastic system is p-ISS/SISS regardless of how often or how seldom the impulses occur. To overcome the difficulties caused by the coexistence of time delays, impulses, and stochastic effects, Razumikhin techniques and piecewise continuous Lyapunov functions as well as stochastic analysis techniques are involved together. An example is provided to illustrate the effectiveness and advantages of our results.http://dx.doi.org/10.1155/2014/589562 |
| spellingShingle | Fengqi Yao Pei Cheng Hao Shen Li Qiu On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays Abstract and Applied Analysis |
| title | On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays |
| title_full | On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays |
| title_fullStr | On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays |
| title_full_unstemmed | On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays |
| title_short | On Input-to-State Stability of Impulsive Stochastic Systems with Time Delays |
| title_sort | on input to state stability of impulsive stochastic systems with time delays |
| url | http://dx.doi.org/10.1155/2014/589562 |
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