Realizations and orientation of implicit systems

The paper considers the problem of model orientation, i.e. the classification of the external signals into inputs and outputs. The problem is considered in the behavioural context where the external model is an autoregressive system. Orientation of a system automatically induces equivalent first order models in state–space or descriptor form via a realization procedure. A new realization procedure is proposed where the realization is implemented in two steps, first an intermediate ARMA realization is obtained. Then, this realization is transformed into the final descriptor system via an appropriate reduction procedure corresponding to the input/output partition of the external variables. Studying the dependency of the resulting system properties and invariants on the different selections of input and output variables and the structure of the initial external behaviour is considered in the paper.