Alternate-continuous-control systems with double-impulse
Abstract We propose a mathematical model that can control the stability of an unstable system. Periodicity is an important feature of the system. We add a continuous control to the first half of each period of the system and then add an impulse control J1 at the 1 / 2 $1/2$ period time. Again, we do...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1340-x |
| _version_ | 1819073660958277632 |
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| author | Xiang Hu Hongjuan Wu Yuming Feng Jiang Xiong |
| author_facet | Xiang Hu Hongjuan Wu Yuming Feng Jiang Xiong |
| author_sort | Xiang Hu |
| collection | DOAJ |
| description | Abstract We propose a mathematical model that can control the stability of an unstable system. Periodicity is an important feature of the system. We add a continuous control to the first half of each period of the system and then add an impulse control J1 at the 1 / 2 $1/2$ period time. Again, we do not control the rest half of each period of the system. Finally, we add an impulse control J2 at the end of each period of the system. The system is called an alternate-continuous-control system with double-impulse. We study the stability of the current system by constructing the Lyapunov function. Using the proposed method, we can control the Chua oscillator. The system has two impulse inputs per period, which is more in line with natural law than the system that only has a single-impulse input. Therefore, the system proposed in this paper is more practical than current mature control systems. |
| first_indexed | 2024-12-21T17:57:10Z |
| format | Article |
| id | doaj.art-4d2725b431934324b431e3d617056c03 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-21T17:57:10Z |
| publishDate | 2017-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4d2725b431934324b431e3d617056c032022-12-21T18:55:10ZengSpringerOpenAdvances in Difference Equations1687-18472017-09-012017111210.1186/s13662-017-1340-xAlternate-continuous-control systems with double-impulseXiang Hu0Hongjuan Wu1Yuming Feng2Jiang Xiong3College of Computer Science and Engineering, Chongqing Three Gorges UniversityCollege of Computer Science and Engineering, Chongqing Three Gorges UniversityKey Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges UniversityCollege of Computer Science and Engineering, Chongqing Three Gorges UniversityAbstract We propose a mathematical model that can control the stability of an unstable system. Periodicity is an important feature of the system. We add a continuous control to the first half of each period of the system and then add an impulse control J1 at the 1 / 2 $1/2$ period time. Again, we do not control the rest half of each period of the system. Finally, we add an impulse control J2 at the end of each period of the system. The system is called an alternate-continuous-control system with double-impulse. We study the stability of the current system by constructing the Lyapunov function. Using the proposed method, we can control the Chua oscillator. The system has two impulse inputs per period, which is more in line with natural law than the system that only has a single-impulse input. Therefore, the system proposed in this paper is more practical than current mature control systems.http://link.springer.com/article/10.1186/s13662-017-1340-xalternate controlcontinuous controldouble-impulseLyapunov functionindex stabilityChua’s oscillator |
| spellingShingle | Xiang Hu Hongjuan Wu Yuming Feng Jiang Xiong Alternate-continuous-control systems with double-impulse Advances in Difference Equations alternate control continuous control double-impulse Lyapunov function index stability Chua’s oscillator |
| title | Alternate-continuous-control systems with double-impulse |
| title_full | Alternate-continuous-control systems with double-impulse |
| title_fullStr | Alternate-continuous-control systems with double-impulse |
| title_full_unstemmed | Alternate-continuous-control systems with double-impulse |
| title_short | Alternate-continuous-control systems with double-impulse |
| title_sort | alternate continuous control systems with double impulse |
| topic | alternate control continuous control double-impulse Lyapunov function index stability Chua’s oscillator |
| url | http://link.springer.com/article/10.1186/s13662-017-1340-x |
| work_keys_str_mv | AT xianghu alternatecontinuouscontrolsystemswithdoubleimpulse AT hongjuanwu alternatecontinuouscontrolsystemswithdoubleimpulse AT yumingfeng alternatecontinuouscontrolsystemswithdoubleimpulse AT jiangxiong alternatecontinuouscontrolsystemswithdoubleimpulse |