Mathematical modelling on Hybrid Dynamical Systems: An application to the bouncing ball and a two-tanks system

Mathematical modeling of Hybrid Dynamical Systems (HDS) aims for describing in a more complete formulation those behaviors composed by discrete and continuous dynamics. This article develops a detailed mathematical description of two systems which exhibit a hybrid behavior through two different models widely known in the HDS theory: The Switched systems and the Hybrid automaton. In addition, some differences and similarities between them are highlighted.