This paper introduces a gearless hydraulic transmission system that provides an infinite speed ratio similar to a Continuous Variable Transmission (CVT) with energy storage capabilities. The transmission system is modeled in various operating conditions such as all-electric and gasoline configurations. A Rate Limited (RL) controller is designed to control the vehicle traction forces. A PI controller is designed to regulate the charge and discharge power through storage and range extender engine in different driving conditions. The results demonstrate high performance operation of the transmission system in standardized drive cycles. The results show that the control system provides a good speed-command tracking performance.