A non-linear dynamic model is developed for a new type of two-wheel vehicles (B2). The B2 has two wheels side by side actuated via two DC motors and commanded through a controller card using a joystick. The vehicle can carry up to two passengers at a time. A first effort has been made to formulate a suitable set of requirements to be followed during the design phase. On the basis of such requirements, a reference linear dynamic model of the B2 has been derived. Then, a model matching H control problem has been solved via the -synthesis approach, which allows disturbance rejection and robustness specifications to be taken into account. Finally, the designed control laws have been evaluated numerically both for the loaded and unloaded vehicle cases. The controller performed well even under maximum uncertainty and perturbation conditions.