This chapter presents the model of a hybrid system to be used in this volume. The focus is on the data structure and on modeling. The model suggests that the flow set, the flow map, the jump set, and the jump map can be specialized to capture the dynamics of purely continuous-time or discrete-time systems on ℝn. The former corresponds to a flow set equal to ℝn and an empty jump set, while the latter can be captured with an empty flow set and a jump set defined as ℝn. In addition, several examples of hybrid systems are given, including models of hybrid control systems. The model of a hybrid system is then related to other modeling frameworks; such as hybrid automata, impulsive differential equations, and switching systems.
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