This paper concerns the estimation of the sideslip dynamics of automotive vehicles in a bounded-error framework. This work considers the linear varying parameter (LPV) model of an automotive vehicle in a polytopic form. This model is obtained by considering the dependency of the model with respect to the vehicle speed as a varying parameter. Since this parameter belongs to a bounded interval (the vehicle speed is obviously bounded by constructor constraints), interval analysis tools propose efficient approaches for estimating the vehicle unmeasured dynamics in all situations. Indeed, in this paper, an estimation strategy is developed to reconstruct the vehicle sideslip dynamical behaviour and then proceed to a stability analysis of the car based on the driving situation. Simulations performed on a nonlinear vehicle model and its parameters (validated by an experimental procedure on a real Renault Megane Coupé) are used to validate the estimation strategy and highlight its efficiency.