For the constant distance spacing policy,the existing researches of the string stability focus on the single-predecessor information framework(SPIF) and predecessor-successor information framework(PSIF).The research results demonstrated that the string stability could not be guaranteed with the SPIF,and then the PSIF was proposed to resolve this string instability.But the issue,whether the string stability can be guaranteed when applying the PSIF,is still controversial.Meanwhile,most of the previous researches on the string stability were conducted without consideration of the parasitic time delays and lags.In this paper,the practical longitudinal vehicle dynamics model is built with consideration of the parasitic time delays and lags existing in the actuators,sensors or the communication systems.Secondly,the detailed theoretical analysis of string stability in frequency domain is conducted to demonstrate that the classical linear control laws can not ensure the string stability when applying both the symmetrical PSIF(SPSIF) and asymmetrical PSIF(APSIF).Thirdly,a control law,which adds the position and velocity information of the leading vehicle,is proposed to guarantee string stability for small/medium platoon,and the other control law,which adds the acceleration information of the controlled vehicle,is proposed to guarantee string stability for large platoon as well as small/medium platoon.Finally,the comparative simulation is conducted to confirm the conducted analysis and the proposed control laws.The conducted research completes the means to analyze the string stability in fiequency domain,provides the parameters' reference for the design and implementation of the practical automatic following controllers,and improves the reliability and stability of the platoon of automatic vehicles.