Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function
This paper deals with stochastically globally exponential stability (SGES) for stochastic impulsive differential systems (SIDSs) with discrete delays (DDs) and infinite distributed delays (IDDs). By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unsta...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/7913050 |
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| _version_ | 1832567870914035712 |
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| author | Xiaoyan Liu Quanxin Zhu |
| author_facet | Xiaoyan Liu Quanxin Zhu |
| author_sort | Xiaoyan Liu |
| collection | DOAJ |
| description | This paper deals with stochastically globally exponential stability (SGES) for stochastic impulsive differential systems (SIDSs) with discrete delays (DDs) and infinite distributed delays (IDDs). By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be coupled with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories. |
| format | Article |
| id | doaj-art-6dd2aca3e4824fed849afcc3ed325e24 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-6dd2aca3e4824fed849afcc3ed325e242025-02-03T01:00:19ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/79130507913050Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov FunctionXiaoyan Liu0Quanxin Zhu1MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, ChinaMOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, ChinaThis paper deals with stochastically globally exponential stability (SGES) for stochastic impulsive differential systems (SIDSs) with discrete delays (DDs) and infinite distributed delays (IDDs). By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be coupled with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories.http://dx.doi.org/10.1155/2020/7913050 |
| spellingShingle | Xiaoyan Liu Quanxin Zhu Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function Complexity |
| title | Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function |
| title_full | Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function |
| title_fullStr | Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function |
| title_full_unstemmed | Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function |
| title_short | Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function |
| title_sort | stochastically globally exponential stability of stochastic impulsive differential systems with discrete and infinite distributed delays based on vector lyapunov function |
| url | http://dx.doi.org/10.1155/2020/7913050 |
| work_keys_str_mv | AT xiaoyanliu stochasticallygloballyexponentialstabilityofstochasticimpulsivedifferentialsystemswithdiscreteandinfinitedistributeddelaysbasedonvectorlyapunovfunction AT quanxinzhu stochasticallygloballyexponentialstabilityofstochasticimpulsivedifferentialsystemswithdiscreteandinfinitedistributeddelaysbasedonvectorlyapunovfunction |