Abstract:The approximately analytical solution for a semiactive suspension system under relative control with timedelay is investigated in this paper. At first, the quartercar model is established and dimensionless analysis is done. Then a system of four nonlinear algebra equations for the approximate solution is obtained by the averaging method, which could be easily treated by numerical methods for algebra equations. At last, the numerical solution of the semiactive relativecontrol suspension system is also obtained through the simulation in MATLAB software. The comparison of the two methods shows the approximately analytical solution is correct and has satisfactory precision.