Analysis and characterisation of hybrid systems with bond-graphs

This paper deals with the analysis of linear hybrid systems. Switching components which modify the circuit topology at switching time, are represented by flow or effort sources, according to their state. Such modelling implies two classes of hybrid systems :-systems whose causality does not change at the commutation, which can be modelled by a state equation with constant order, but variable parameters according to the mode;-systems whose integral causality changes, which can be modelled by a state equation with variable order and variable parameters. For that class of systems, there are some Dirac pulses on variables at the commutation. A solution is proposed to compute the amplitude of the pulse and the value of the new variables using the equation formulation from bond-graphs