In this paper, control oriented rational tyre models are developed and incorporated in the design of vehicle dynamics estimators and controllers. Previously proposed rational models are used to derive a generic rational tyre model whose parameters are obtained through the optimisation of an increased number of regression terms. The proposed model results in vehicle dynamic responses that closely follow those obtained with a Magic Formula tyre model for a range of driving scenarios, especially on low mu roads. The usage of rational tyre models in the design of again-scheduled active front steering controller working in coordination with a nonlinear observer is demonstrated in the second part of the paper where the vehicle model is expressed as a linear parameter varying system. This final step demonstrates the strength of the rational tyre models' selected structure allowing the estimation of vehicle states through the estimation of the road adhesion coefficient which is obtained by simple algebraic computations.