In automotive drive systems, differential gear backlash degrades the control performance. Specifically, a shock torque, which is generated when the gear runs freely and collides with the backlash, increases the vibration amplitude. Consequently, it is important to develop a vibration control method to suppress the adverse effect of nonlinearity due to backlash. Furthermore, considering implementations on actual vehicles, design at the development site, and mass production, a simple and practical control method is necessary. This paper describes the configuration of a basic experimental device, which abstracts an actual vehicle to focus on the influence due to backlash while reflecting the basic structure of an automotive drive system. Next, a basic controller is designed using a mixed H_2/H_? control theory, and a servo system is constructed to track the target value. A simple control mode switching algorithm is proposed for backlash compensation. This algorithm is suited to practical applications because it uses only an output without a state estimation and it compensates for performance deteriorations due to the nonlinearity by operating a single linear controller. Finally, simulations and experiments verify the effectiveness of the proposed control system.