Response of Duffing system with delayed feedback control under bounded noise excitation

This paper presents a procedure for predicting the response of Duffing system with time-delayed feedback control under bounded noise excitation by using stochastic averaging method. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged It stochastic differential equations for the system are derived by using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov equation associated with the averaged It equations. It is shown that the time delay in feedback control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing system. The validity of the proposed method is confirmed by digital simulation.