This paper presents an LMI based robust H-infinity control scheme for constrained systems with norm-bounded uncertainties. The uncertainties are incorporated in the evaluation of the H-infinity norm and the time-domain constraints. The robust closed-loop properties inclusive of stability, H-infinity performance and the satisfaction of the time-domain constraints are discussed. Analysis and simulation results for a 2 DOF quarter-car model show possible improvements on ride comfort, while robustly respecting safety related constraints such as good road holding, limited suspension strokes and actuator saturation.