Mathematical Structures in the Network Representation ofEnergy - Conserving Physical

It is shown that network modelling of energy-conserving physical systems naturally leads to the consideration of (nonlinear) implicit generalized Hamilto-nian systems. Behavioral systems theory may be invoked to formulate and analyze the system-theoretic properties of these systems. Most of the current modelling approaches of physical systems (e.g. multi-body systems) are based on some sort of network representation, where the physical system under consideration is seen as the interconnection of a possible large number of simple subsystems (the elementary building blocks). This way of modelling has several advantages. The knowledge about subsystems can be stored in libraries, and is re-usable for later occasions. Because of the modularity the modelling process can be performed in a \recursive" manner, rst neglecting certain eeects and gradually reening the model by adding other subsystems. Further, the approach is suited to general control design where the overall behavior of the system is sought to be improved by the addition of other subsystems (controllers). have mainly concentrated on energy-conserving physical systems, where we have argued that the basic dynamic building blocks are of the form 8 < : _ x = J(x) @H @x (x) + g(x)f e = g T (x) @H @x (x) (1)