Connected and automated vehicles (CAVs) and regular human-piloted vehicles (RVs) will coexist in the near future. Research has indicated the feasibility of using CAVs to stabilize traffic flow and eliminate stop-and-go waves. In light of this, we develop distributed control schemes to stabilize mixed vehicular platoons by using CAV as the leading vehicle. We address several challenges, such as limited information perception capabilities of RVs, the uncertain actuation of human drivers, and external disturbances. Only local information from the preceding vehicle is used in the controllers. Modifications of the input-to-state string stability (ISSS) are established to cope with the uncertainty and disturbance characteristics while conditions for stability are derived. The proposed control schemes can attenuate the effect of disturbances while maintaining the ISSS property. The relationships between ISSS and other string stability concepts are clarified. Finally, numerical experiments are conducted to validate the effectiveness of the proposed platoon control schemes.