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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ning Tian & Xiaoqi Liu & Rui Kang & Cheng Peng & Jiaxi Li & Shang Gao, 2024. "Noise-to-State Stability of Random Coupled Kuramoto Oscillators via Feedback Control," Mathematics, MDPI, vol. 12(23), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3715-:d:1530365
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