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Automatic driving has received a broad of attention from academia and industry since it is effective in greatly reducing the severity of potential traffic accidents and achieving the ultimate automobile safety and comfort. This article presents a back‐stepping sliding mode controller (BSMC) through linear matrix inequalities (LMIs) for the highly automatic driving vehicle on sloped roads. It includes three key modules, namely, an extended Kalman filter (EKF)‐based road slope estimation module, a robust BSMC‐LMIs velocity‐tracking controller based on the input–output feedback linearization, as well as a longitudinal inverse vehicle dynamics module. The nonlinear combined slip tire model with the transient behavior is introduced to calculate the tire forces properly, which would be further proven to offer more accurate road slope estimations even in a fierce acceleration or deceleration situation. The proposed BSMC …