Finite-time stability and settling-time estimation of nonlinear impulsive systems
This paper studies the problem of finite-time stability (FTS) for nonlinear impulsive systems. Based on impulsive control theory, several Lyapunov-based FTS theorems involving stabilizing impulses and destabilizing impulses are established, respectively. Our proposed results provide sufficient condi...
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| Published in | Automatica (Oxford) Vol. 99; pp. 361 - 368 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.01.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1098 1873-2836 |
| DOI | 10.1016/j.automatica.2018.10.024 |
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| Abstract | This paper studies the problem of finite-time stability (FTS) for nonlinear impulsive systems. Based on impulsive control theory, several Lyapunov-based FTS theorems involving stabilizing impulses and destabilizing impulses are established, respectively. Our proposed results provide sufficient conditions for estimating the settling-time with respect to suitable classes of impulse time sequences. It is shown that the settling-time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect. As compared with the case without using stabilizing impulses, a smaller bound of setting-time can be derived when a FTS system is subject to stabilizing impulses. Conversely, a larger bound of settling-time can be derived when the FTS system is subject to destabilizing impulses, as compared with the case without using destabilizing impulses. As a special case, we extend the ideas to nonlinear impulsive delay systems and derive some delay-independent FTS results. Examples and their simulations are given to demonstrate the applicability of the proposed results. |
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| AbstractList | This paper studies the problem of finite-time stability (FTS) for nonlinear impulsive systems. Based on impulsive control theory, several Lyapunov-based FTS theorems involving stabilizing impulses and destabilizing impulses are established, respectively. Our proposed results provide sufficient conditions for estimating the settling-time with respect to suitable classes of impulse time sequences. It is shown that the settling-time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect. As compared with the case without using stabilizing impulses, a smaller bound of setting-time can be derived when a FTS system is subject to stabilizing impulses. Conversely, a larger bound of settling-time can be derived when the FTS system is subject to destabilizing impulses, as compared with the case without using destabilizing impulses. As a special case, we extend the ideas to nonlinear impulsive delay systems and derive some delay-independent FTS results. Examples and their simulations are given to demonstrate the applicability of the proposed results. |
| Author | Ho, Daniel W.C. Cao, Jinde Li, Xiaodi |
| Author_xml | – sequence: 1 givenname: Xiaodi surname: Li fullname: Li, Xiaodi email: lxd@sdnu.edu.cn organization: School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, PR China – sequence: 2 givenname: Daniel W.C. surname: Ho fullname: Ho, Daniel W.C. email: madaniel@cityu.edu.hk organization: Department of Mathematics, City University of Hong Kong, Hong Kong, China – sequence: 3 givenname: Jinde surname: Cao fullname: Cao, Jinde email: jdcao@seu.edu.cn organization: The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics, Southeast University, Nanjing 210096, PR China |
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| Snippet | This paper studies the problem of finite-time stability (FTS) for nonlinear impulsive systems. Based on impulsive control theory, several Lyapunov-based FTS... |
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| SubjectTerms | Finite-time stability Lyapunov theorems Nonlinear impulsive systems Settling-time Time delay |
| Title | Finite-time stability and settling-time estimation of nonlinear impulsive systems |
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