Balanced model reduction of symmetric composite systems

Abstract

In this paper, we investigate the structural properties of balanced realizations, and their truncation, of a class of systems with symmetric interconnected and identical structure. It is established that the balanced realizations of such symmetric composite systems can be constructed via the balanced realizations of two auxiliary systems of comparatively low dimensions. The corresponding truncated realizations, which also have a certain symmetric structure, are explicitly constructed. The extension of the results to generalized symmetric composite systems is also studied.