Abstract: A new method is proposed to develop a generalized mixed H₂/H_∞ controller which considers both input time delay and parameter uncertainty,and it is applied to active vehicle suspensions design.It is assumed that the time delay of actuator is an uncertain constant value with a known constant boundary,and the uncertain parameter of the system is norm-bounded.As required for the design of the suspensions,the H_∞ and the generalized H₂ performance indicators are used respectively to reflect the sprung mass acceleration and the design constraints of the mechanical structure.The two performance indicators of the closed-loop system are met simultaneously by defining a Lyapunov function,and the designing of a generalized mixed H₂/H_∞ controller is transformed into the solution of the inequalities linear matrix.The simulation is made on a two degree-of-freedom quarter-car suspension model,and the results show that the designed controller can always achieve good performance regardless of the bounded time-delay and the variation of the parameters.