Potential Impacts of Delay on Stability of Impulsive Control Systems
In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability a...
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| Published in | IEEE transactions on automatic control Vol. 67; no. 10; pp. 5179 - 5190 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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New York
IEEE
01.10.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive time-delay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid impulses, which contain both stabilizing impulses and destabilizing impulses. Three illustrative examples are presented to reveal the potential impacts of delay on the stability of impulsive control systems. |
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| AbstractList | In this article, the exponential stability of impulsive control systems with time delay is studied. By using the average impulsive interval method, some sufficient Lyapunov-based conditions are established for the stability of impulsive time-delay systems, and the impacts of delay on the stability analysis method are further revealed. It is interesting to show that some unstable impulsive time-delay systems may be stabilized by increasing the time delay in continuous dynamics. More interestingly, it is proved that along with the increase of the delay within a certain range, the convergence rate of such impulsive time-delay systems also increases correspondingly. Further, a strict comparison principle for impulsive control systems with delay is established. Then by utilizing this comparison principle, it can be shown that for some stable impulsive systems with delay, under certain conditions, the stability is robust against any large but bounded delay. Compared with the previous results on delay-free impulsive systems, some potential impacts of delay on the stability are investigated. Particularly, the obtained results are extended to the case of impulsive control systems with hybrid impulses, which contain both stabilizing impulses and destabilizing impulses. Three illustrative examples are presented to reveal the potential impacts of delay on the stability of impulsive control systems. |
| Author | Lu, Jianquan Jiang, Bangxin Zheng, Wei Xing |
| Author_xml | – sequence: 1 givenname: Jianquan orcidid: 0000-0003-4423-6034 surname: Lu fullname: Lu, Jianquan email: jqluma@gmail.com organization: Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China – sequence: 2 givenname: Bangxin orcidid: 0000-0002-6900-980X surname: Jiang fullname: Jiang, Bangxin email: jiangbangxin@163.com organization: Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China – sequence: 3 givenname: Wei Xing orcidid: 0000-0002-0572-5938 surname: Zheng fullname: Zheng, Wei Xing email: w.zheng@westernsydney.edu.au organization: School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, NSW, Australia |
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| SubjectTerms | Average impulsive interval (AII) Control systems Delay effects Delays exponential stability Geophysical measurement techniques Germanium Ground penetrating radar hybrid impulses Hybrid systems Impulses impulsive control Principles Stability analysis Stability criteria Time delay systems |
| Title | Potential Impacts of Delay on Stability of Impulsive Control Systems |
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