For a quarter car with nonlinear active suspension in rough road, the problem of random modeling and control is considered.\nAccording to the relative motion principle, the influence of rough road can be seen as that force is disturbed by the noise and a\nrandom model is constructed. By an appropriate transform, the model is transformed into a lower triangular system, which can\nbe used as backstepping method. Then a controller is designed such that the mean square of the state converges to an arbitrarily\nsmall neighborhood of zero by tuning design parameters. The simulation results illustrate the effectiveness of the proposed scheme.\nTherefore, the active suspension system offers better riding comfort and vehicle handing to the passengers.
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