On representations of linear dynamic networks

Linear dynamic networks are typically described in either a state-space form or a module representation. The question is addressed under which conditions these representations are equivalent and can be transformed into one another. Hidden states and especially shared hidden states have a central position in this analysis. A consequence for identification is that MIMO parameterised modules may be necessary in order to appropriately take care of shared hidden states. Further, the construction of sub-networks in a linear dynamic network resulting in a module representation is illustrated. The module dynamic network allows to zoom in/out on/of the network to include/exclude more detailed structural information. Zooming in and out is respectively described by realisation and multi-path immersion.