This paper formulates the active suspension control problem as disturbance attenuation problem with output and control constraints. The H performance is used to measure ride comfort such that more general road disturbances can be considered, while time-domain hard constraints are captured using the concept of reachable sets and state-space ellipsoids. Hence, conflicting requirements are specified separately and handled in a nature way. In the framework of Linear Matrix Inequality (LMI) optimization, constrained H active suspensions are designed on half-car models with and without considering actuator dynamics. Analysis and simulation results show a promising improvement on ride comfort, while keeping suspension strokes and control inputs within bounds and ensuring a firm contact of wheels to road.

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