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Hybrid systems are systems that exhibit a combination of discrete and continuous behavior. Typical hybrid systems include computer components, which operate in discrete program steps, and real-world components, whose behavior over time intervals evolves according to physical constraints. Important examples of hybrid systems include automated transportation systems, robotics systems, process control systems, systems of embedded devices, and mobile computing systems. Such systems can be very complex, and very difficult to describe and analyze. This paper presents the Hybrid Input/Output Automaton (HIOA) modeling framework, a basic mathematical framework to support description and analysis of hybrid systems. An important feature of this model is its support for decomposing hybrid system descriptions. In particular, the framework includes a notion of external behavior for a hybrid I/O automaton …