Energetic balance in hybrid systems using bond graph

This paper deals with the modeling of switching systems (a class of hybrid dynamical systems) using the bond graph formalism. When the switching components are modeled using an ideal representation a variable topology system is obtained. If the system has n valid modes, we have n different state equations and variable states may be discontinuous at the commutation. The purpose of this article is to establish the energetic balance at the commutation time and to compare the ideal approach with a classical approach that consists in modeling the switches using variables resistances. Some example allows to compare these points of view