Abstract: In this paper, taking the vehicle active suspension system considering time delay as the research object, by the method of combining theory and experiment, the influence of time delay on the vibration characteristics of the suspension system is studied. Firstly, the dynamic model of the active suspension system with time delay is established. Based on H_∞ control theory, through Lyapunov -Krasovskii function and free weight matrix method, the matrix inequality of asymptotically stable closed-loop system with time-delay is derived, and the H_∞ control law with known maximum stable time-delay is designed. Then, the numerical simulation and experimental method are used to verify the control law. The results show that H_∞ control law can effectively suppress the sprung mass acceleration. Finally, the relationship between the time delay and the root mean square value of the sprung mass acceleration is analyzed under different gain and it is found that the closer the time delay is to τ_max for gain control, the better the control effect

Key words: active suspension, time delay, H_∞ control, time delay feedback test