Automotive engine models vary in their complexity depending on the intended application. Pre-prototype performance prediction models can be very complex in order to make accurate predictions. Controller design models need to be as simple as possible since model-based controllers must operate in real time. This paper develops hybrid models for engine control that incorporate time and events in their formulation. The resulting hybrid controllers have the capability of switching between two alternative control modes. The first mode is designed to reduce the raw hydrocarbon (HC) emissions while the second mode tries to increase the temperature of the catalytic converter as rapidly as possible during the initial transient or "cold start'' period. Reachability, as a tool for system analysis, is used to verify the properties of the closed loop system.