Based on the guaranteed cost theory, this paper proposes a robust controller for the automotive electrohydraulic coupling system. However, parameter perturbation caused by the model linearization is a critical challenge for the nonlinear electrohydraulic coupling system. Generally, the electrical brake booster system (E-booster) can be separated into three parts, a permanent magnet synchronous motor (PMSM), a hydraulic model of the master cylinder, and the transmission mechanism. In this paper, the robust guaranteed cost controller (RGCC) is adopted to achieve an accurate regulation of the pushrod position of the E-booster and has strong robustness against internal uncertainties, and the linear extended state observer (LESO) is utilized to optimize E-booster's dynamic performance. Specifically, the tracking differentiator (TD) and LESO are used to improve the dynamic precision and reduce the hysteresis effect. The overshoot is suppressed by TD, and the disturbance caused by nonlinear uncertainty is restrained by LESO. The experimental results show that RGCC sacrifices a 6% phase lag in the low-frequency domain for a 10% and 40% reduction in first and second-order, respectively, compared with the proportion integration differentiation (PID). Results demonstrate that RGCC has higher precision and stronger robustness in dynamic behavior.