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This paper presents the robustness analysis for the head-to-tail string stability of connected cruise controllers that utilize motion information of human-driven vehicles ahead. In particular, we consider uncertainties arising from the feedback gains and reaction time delays of the human drivers. We utilize the linear fractional transformation and the M-∆ uncertain interconnection structure to represent the uncertainties in the block-diagonal matrix ∆. The uncertain gains are directly incorporated in the uncertain interconnection structure, while the uncertain time delays are taken into account using the Rekasius substitution that preserves the tightness of the robustness bounds. This modeling framework scales well for large-size connected vehicle systems. We demonstrate through two case studies how parameters in the connected cruise controller can be selected to ensure robust string stability. Theoretical results are supported by experiments that highlight the advantage of robust control designs.