Stationary response of nonlinear Markovian jump system under wide-band random excitation

An approximate procedure for predicting the stationary response of a stochastically excited nonlinear Markovian jump system under wide-band random excitation is proposed. Firstly, a weighted-average system in probability can be established to approximate the original one. Then by using the stochastic averaging method, the weighted-average system was reduced to the one described by a one-dimensional averaged Ito equations. The approximate stationary probability densities of the original system are obtained for different jump rules by solving the associated Fokker-Plank-Kolmogorov equation. Finally, an example of Markovian jump Duffing system excited by wide-band random excitation to illustrate the proposed method in detail and the effectiveness of the proposed method is verified via comparing the analytical results with those from Monte Carlo simulation.