Response and reliability analysis of random time-delay controlled systems undergo wide-band random excitations

This paper proposed a new procedure for response and reliability analysis of a multi-degree-of-freedom (MDOF) random time-delay controlled nonlinear system subjected to wide-band random excitations. A two-steps method is presented to deal with random time delay: Firstly, by modeling the random jump time-delay as a Markov jump process, the random delayed control is formulated as the one with discrete Markov jump varying delay; secondly, based on the randomly periodic property of the system, the Markov jump delay is taken out of the control as a parameter. A new scheme based on limit averaging and stochastic averaging principle is developed, which suppresses the rapidly varying processes to generate a less-dimensional probability-weighted system. The Fokker–Planck–Kolmogorov (FPK) equation and the backward Kolmogorov (BK) equation are then deduced and solved, from which the quantitative characteristics of the response and reliability of the system are obtained. Finally, an example is worked out in detail, from which the application and effectiveness of the proposed method are demonstrated.