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This paper investigates control design for the platoon of automated vehicles whose sensors have limited sensing capability. A novel hybrid platoon model is established, in which actuator delay (e.g., the fueling and braking delay) and the effect of sensing range limitation are involved. Based on the new model, a framework of guaranteed-cost controller design is presented, which can robustly stabilize the platoon of vehicles with a given level of disturbance attenuation. The obtained controller is complemented by additional conditions that were established to guarantee string stability and zero steady-state spacing error, yielding a useful string-stable platoon control algorithm. The effectiveness and advantage of the presented methodology is demonstrated by both numerical simulations and experiments with laboratory-scale Arduino cars.