The concept of autonomous driving has gained increasing relevance, leading to a need for the development of innovative drive concepts for motor vehicles. Therefore, this paper presents a model-based optimal multivariable control for the wheel slip, which allows specifying the wheel slip and thus the tire force individually for each wheel. The plant model consists of a multibody two-track model of a vehicle, a tire model, an air resistance model and a motor model. In addition, the contact forces of the individual wheels are calculated dynamically. The resulting nonlinear model is linearized and used for the design of a linear optimal static state space controller with reference and disturbance feedforward. The contact point velocities at the wheels are defined as the controlled variables, since they are proportional to the wheel slip and thus to the driving forces within the operating range of the controller. In addition, the rates of change of the contact point velocities are also chosen as controlled variables to set damping of the closed-loop system. The four drive torques of the wheels represent the control variables. Therefore, a true multivariable control is developed. In the first step of the analysis, the linearized closed-loop system is investigated regarding stability, robustness and its dynamic behavior. The control system shows a high bandwidth, a well damped dynamic behavior and a large phase margin. In the second step of the analysis, various simulations of realistic experiments, such as an accelerated cornering maneuver or the Fishhook road test, are performed with the nonlinear closed-loop system. The results of these experiments confirm the high robustness and good dynamic behavior of the control system in most cases. Moreover, the results demonstrate how the control considers the dynamic contact forces of the wheels to achieve the requested wheel slip at any time. Lastly, dominant transfer paths are identified based on the gain matrix of the state space controller, showing which input and state variables have significant influence on the control variables. Based on this, single-input single-output controls for the individual wheels can be derived.