In this paper, the problem of vehicle sideslip angle estimation is studied based on a single-track model, and an approach to robust H filter design with sampled-data measurements is proposed. Considering the changes of the vehicle mass, the moment of inertia about the yaw axis and the nonlinear relationships between the road surface and tyres, the vehicle lateral dynamics are characterized by a system with parameter uncertainties, which belong to a given convex polytope. By utilizing an input delay approach, the filtering error system is transformed into a continuous-time system with time delay in the state. By introducing a Lyapunov–Krasovskii functional and a free weighting matrix technique, LMI-based conditions have been formulated for the stability analysis of the filtering error system and the existence of admissible filters, which ensure the filtering error system is asymptotically stable with a prescribed H disturbance attenuation level. Finally, some simulation results are provided to illustrate the effectiveness of the proposed method.