This paper suggests a constrained H∞ control scheme for active suspensions with output and control constraints. The H∞ performance is used to measure ride comfort so that more general road disturbances can be considered. Time-domain constraints, representing requirements for: 1) good road holding which may have an impact on safety; 2) suspension stroke limitation; and 3) avoidance of actuator saturation, are captured using the concept of reachable sets and state-space ellipsoids. The proposed approach can potentially achieve the best possible ride comfort by allowing constrained variables free as long as they remain within given bounds. A state feedback solution to the constrained H∞ active suspension control problem is derived in the framework of linear matrix inequality (LMI) optimization and multiobjective control. Analysis and simulation results for a two-degree-of-freedom (2-DOF) quarter-car model show possible improvements on ride comfort, while respecting time-domain hard constraints.