Stabilization problem of stochastic time-varying coupled systems with time delay and feedback control

Abstract

The stabilization of stochastic coupled systems with time delay and time-varying coupling structure (SCSTT) via feedback control is investigated. We generalize systems with constant coupling structure to the time-varying coupling structure. Combining the graph theory with the Lyapunov method, a systematic method is provided to construct a Lyapunov function for SCSTT, and a Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilization in the sense of pth moment exponential stability. Furthermore, theoretical results are applied to analyze the stabilization of stochastic-coupled oscillators with time delay and time-varying coupling structure in order to illustrate the practicability of the results. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of theoretical results.

Keywords:

• Time-varying coupling structure
• time delay
• feedback control
• stabilization
• stochastic coupled systems

AMS Subject Classifications:

• 45R05
• 60H20
• 93D15

Acknowledgements

The authors would like to thank the reviewer for his very helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the NNSF of China [grant number 11401136]; the NNSF of Shandong Province [grant number ZR2014AQ010], [grant number ZR201702090112]; China Postdoctoral Science Foundation funded project; the Key Project of Science and Technology of Weihai [grant number 2015DXGJMS08] and HIT.IBRSEM. A. 2014014.