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Abstract. This paper deals with the modelling of hybrid physical systems. The bond graph technique is used to establish their knowledge model, based upon an ideal representation of the switches. These components are either modelled by flow or by effort sources according to their state, and therefore modify the circuit topology at switching times. The paper shows the usefulness of the implicit representation to derive a unique implicit state equation with jumping parameters, to analyse the model properties, to derive an implicit state equation with nilpotency index one for each configuration, and to compute the discontinuities. Besides, a comparison between the chosen ideal modelling approach and the more common non ideal one is carried out using singular perturbations theory. After a presentation of the whole study in the most general context, its results are applied to power converters, which constitute a particular class of hybrid physical systems where switches only commutate by pairs. Lastly, an example is developed.

In this paper we extend a technique developed to design a feedback stabilizing control law for autonomous switched systems all modes of which are unstable. More specifically, we extend the switching table procedure to the class of affine switched systems, the dynamics of which either do not have an equilibrium point or, if they do, it is not common. This method is then applied to the DC-DC buck-boost converter. The design of the control law is based on dynamic programming and it results in a partition of the state space into switching look-up tables. A comparison with a Lyapunov based technique is also discussed