||This paper deals with the state estimation and control problem for nonlinear lateral vehicle dynamics with time delays. First, a novel time-varying delay vehicle model described as a Takagi-Sugeno fuzzy model is presented. In particular, it is considered that the lateral force contains an air resistance term which is assumed to be a quadratic function of the lateral vehicle velocity. A time-varying delay has been included in the vehicle states by a simple formula in order to capture brake actuation aspects or other practical aspects that may generate a delayed response, while the nonlinear part of the vehicle model is described as a Lipschitz function. A Takagi-Sugeno time-delay observer-based control that satisfies the Lipschitz condition is proposed to get closed-loop stability conditions. These results generalize existing ones in the literature on lateral dynamics control. Additionally, we provide a new methodology for the controller and observer gains design that can be cast as linear matrix inequality constraints. Finally, we illustrate our results with numerical examples, which also reveal the negative effect of not considering the presence of delays in the controller design.