Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control
This paper is intended to study noise-to-state stability in probability (NSSP) for random coupled Kuramoto oscillators with input control (RCKOIC). A feedback control is designed, which makes us give the existence and uniqueness of a solution for RCKOIC. Based on Kirchhoff’s matrix tree theorem in g...
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MDPI AG
2024-11-01
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| Online Access: | https://www.mdpi.com/2227-7390/12/23/3715 |
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| author | Ning Tian Xiaoqi Liu Rui Kang Cheng Peng Jiaxi Li Shang Gao |
| author_facet | Ning Tian Xiaoqi Liu Rui Kang Cheng Peng Jiaxi Li Shang Gao |
| author_sort | Ning Tian |
| collection | DOAJ |
| description | This paper is intended to study noise-to-state stability in probability (NSSP) for random coupled Kuramoto oscillators with input control (RCKOIC). A feedback control is designed, which makes us give the existence and uniqueness of a solution for RCKOIC. Based on Kirchhoff’s matrix tree theorem in graph theory, an original and appropriate Lyapunov function for RCKOIC is established. With the help of the Lyapunov method and by resorting to some analysis skills, NSSP for RCKOIC with an arbitrarily coupled topological structure and second-order moment process stochastic disturbance is acquired. Finally, the effectiveness of the obtained results is verified by a numerical test and its simulation process. |
| format | Article |
| id | doaj-art-ab6934cff5d74b5bad7128e669fcbef9 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-ab6934cff5d74b5bad7128e669fcbef92025-08-20T02:50:38ZengMDPI AGMathematics2227-73902024-11-011223371510.3390/math12233715Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback ControlNing Tian0Xiaoqi Liu1Rui Kang2Cheng Peng3Jiaxi Li4Shang Gao5Department of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaThis paper is intended to study noise-to-state stability in probability (NSSP) for random coupled Kuramoto oscillators with input control (RCKOIC). A feedback control is designed, which makes us give the existence and uniqueness of a solution for RCKOIC. Based on Kirchhoff’s matrix tree theorem in graph theory, an original and appropriate Lyapunov function for RCKOIC is established. With the help of the Lyapunov method and by resorting to some analysis skills, NSSP for RCKOIC with an arbitrarily coupled topological structure and second-order moment process stochastic disturbance is acquired. Finally, the effectiveness of the obtained results is verified by a numerical test and its simulation process.https://www.mdpi.com/2227-7390/12/23/3715noise-to-state stabilityrandom coupled Kuramoto oscillatorsfeedback controlLyapunov methodKirchhoff’s matrix tree theorem |
| spellingShingle | Ning Tian Xiaoqi Liu Rui Kang Cheng Peng Jiaxi Li Shang Gao Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control Mathematics noise-to-state stability random coupled Kuramoto oscillators feedback control Lyapunov method Kirchhoff’s matrix tree theorem |
| title | Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control |
| title_full | Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control |
| title_fullStr | Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control |
| title_full_unstemmed | Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control |
| title_short | Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control |
| title_sort | noise to state stability of random coupled kuramoto oscillators via feedback control |
| topic | noise-to-state stability random coupled Kuramoto oscillators feedback control Lyapunov method Kirchhoff’s matrix tree theorem |
| url | https://www.mdpi.com/2227-7390/12/23/3715 |
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