Discretely controlled continuous systems are characterised by their interacting continuous and discrete dynamics, where the continuous subsystem usually represents the system to be controlled and the discrete part describes the controller that switches the continuous system among different operation modes. This paper analyses systems where a perpetual switching of the operation mode has to occur in order to maintain the system's state in a prescribed operating region. It is shown how the analysis of the overall hybrid system can be simplified by using an embedded map that determines the behaviour at the switching instants.