Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control

Ning Tian, Xiaoqi Liu, Rui Kang, Cheng Peng, Jiaxi Li and Shang Gao ()
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Ning Tian: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Xiaoqi Liu: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Rui Kang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Cheng Peng: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Jiaxi Li: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Shang Gao: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2024, vol. 12, issue 23, 1-10

Abstract: 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.

Keywords: noise-to-state stability; random coupled Kuramoto oscillators; feedback control; Lyapunov method; Kirchhoff’s matrix tree theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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