A stochastic averaging technique for resonant and non-resonant quasi linear systems subject to multi-time-delayed feedback control and wide-band random excitation is developed. The technique is then applied to predict the response of one and two degree-of-freedom linear oscillators with nonlinear dampings subject to wide-band random excitations and multi-time-delayed feedback control. It is shown through comparison with the result from Monte Carlo simulation that the proposed technique yields quite a good result, even for long delay time, and that the time-delayed feedback control may result in phenomenological bifurcation.
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