Non-smooth structured robust controller design has drawn a lot of attention recently due to its ability to deal with uncertainty and its convenience for implementation. In this paper, the method is extended to design the structured robust linear parameter-varying (LPV) estimator by pulling out scheduling variables from estimator using linear fractional transformation (LFT). The structured robust LPV estimator is then applied to vehicle sideslip angle estimation. Both the measured vehicle speed and estimated tire cornering stiffness are treated as scheduling variables to further reduce sideslip angle estimation error. The effects of estimator order and number of repetitiveness of scheduling variables are studied using a MATLAB/Simulink bicycle model. The developed approach is later verified in Hardware-in-the-Loop (HIL) simulation environment using dSPACE SCALEXIO and MicroAutoBox. A comprehensive high-fidelity dSPACE automotive simulation models (ASM) vehicle model is used for the real-time HIL simulation. Double-lane change and sine steer maneuvers have been implemented to verify the effectiveness of the structured robust LPV sideslip angle estimation method.