Minimal realizations of interconnected dynamical systems

The problem of minimal realization (MR) for interconnected dynamical systems (IDS) with component-connection model (CCM) is studied in this paper. CCM is a structural approximation that considers the IDS composed by two contributions: one, related with the components (or subsystems) represented by a dynamic first order model and, the other, related with the connections among the components, with a linear algebraic model. The main CCM feature is information decoupling, which is done by separating the dynamics of the components from the system topology. In this context, obtaining a system order reduction is highly desirable given the dimensions of the interconnected system. In this paper, several alternative procedures for obtaining a MR according to the phase of the CCM considered are proposed and developed. These procedures were implemented in a MATLAB toolbox developed by the author and were applied to solve several cases under study. The results allow the establishment of characteristics and properties of the MR for CCM. These results agree with those reported using other methods of order reduction, especially in the matter of the equivalence among procedures.