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This paper considers the robustness analysis and distributed 'I-1 _∞ (H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure γ-gain, and introduce a scalable multistep procedure to synthesize a distributed 'I-1 _∞ controller for large-scale platoons. It is shown that communication topology, especially the leader's information, exerts great influence on both robustness performance and controller synthesis. Furthermore, an intuitive optimization problem is formulated to optimize an …