Integrated motor-transmission (IMT) system is prone to suffer from torsional oscillations due to its fast dynamic behavior and weak damping characteristics. Meanwhile, signal communication between sensors, controllers and actuators via controller area network (CAN) that introduces time-varying delays, could also stimulate torsional oscillations in IMT system. Thus, this paper is intended to develop a robust controller to suppress these oscillations for IMT system during vehicle speed tracking. Considering the coupling effects of CAN-induced time-varying delays and event-driven manner of the controller nodes, as well as possible sampling period change, a delay-free discrete time model is built for IMT system by using polytopic inclusion approach and system augmentation technique. Based on this model, an energyto-peak performance based robust controller is then developed for IMT system over CAN. It can achieve stable as well as good torsional oscillations suppression performance in spite of CAN-induced time-varying delays, sampling period change and also measurement noises. Finally, with a detailed CAN model developed by using SimEvent, conventional proportional-integral (PI) controller and energy-to-peak controller that designed with fixed sampling period are utilized in the comparative tests to show the effectiveness as well as performance of proposed torsional oscillations controller. INDEX TERMS Torsional oscillations, robust energy-to-peak control, polytopic inclusion approach, controller area network, integrated motor-transmission.