The market development of partially electrified powertrains in passenger cars motivates the re-consideration of the idle speed control problem. In this paper, a switching system model is first developed to unite the main discrete-event characteristics of the combustion engine and time-continuous characteristics of the electric motor. The presented model is classified as a discrete-time switching system model with linear subsystems.Based on this description, we further perform a model-based controller design using the lifting technique. Although the optimality property of the controller is bound to the assumption of constant turning speed, it still provides several useful properties. These are the inherent control allocation between electric and combustion engine, the consideration of the discontinuous behavior, and the discrete-time description basis which is important for implementation in a common controller architecture.