Interconnection of systems: the network paradigm

In this paper we propose first to recall the different interconnection structures appearing in network models and to show their exact correspondence with Dirac structures. This definition of interconnection is purely implicit hence does not discriminate between inputs and outputs among the interconnection variables and describes the relations between in an implicit form as some geometric space. Secondly we extend the definition of network interconnection by considering the variables defining the energy as belonging to Lie groups and will show that this leads to consider interconnection as Dirac structure on some Lie algebras.