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The design of engine control systems has been traditionally carried out using a mix of heuristic techniques validated by simulation and prototyping using approximate average-value models. However, the ever increasing demands on passengers' comfort, safety, emissions, and fuel consumption imposed by car manufacturers and regulations call for more robust techniques and the use of cycle-accurate models. We argue that these models must be hybrid because of the combination of time-domain and event-based behaviors. We present a hybrid model of the engine in which both continuous and discrete time-domain as well as event-based phenomena are modeled in a separate but integrated manner. Based on this model, we formalize the specification of the overall engine control by defining a number of hybrid control problems. To cope with the difficulties arising in the design of hybrid controllers, a design methodology is proposed. This methodology consists of a relaxation of the hybrid problem by simplifying some of its components to obtain a solvable problem,and then deriving a solution to the original control problem by appropriately modifying the control law so obtained to take into consideration the original specifications and models. The effectiveness of this approach is illustrated on three challenging problems: fast force-transient control, cutoff control, and idle speed control.