Stationary distribution for stochastic coupled systems with regime switching and feedback control

The existence of stationary distribution for stochastic coupled systems with regime switching and feedback control is investigated. In terms of model, feedback control is concerned in the existence of stationary distribution for stochastic coupled systems with regime switching. In terms of method, graph theory is employed to investigate the existence of stationary distribution for stochastic coupled systems with regime switching. And some sufficient conditions are given based on Lyapunov method connected with the graph theory and the M-matrix method to ensure the existence of stationary distribution, which reveals the influences that feedback control brings on stationary distribution and the existing area is related to stochastic disturbance, feedback control and coupling strength. Furthermore, the application to stochastic coupled oscillators with feedback control and regime switching can demonstrate the practicability of our theoretical results. Finally, a numerical example is presented to verify the effectiveness and availability of our results as well as the superiority of influence that feedback control brings on stationary distribution.