On the global properties of interconnected systems

Interconnected systems are discussed in terms of their global properties. A theory of signal flow graphs over rings is developed. A new sufficient condition is derived for the complete reducibility of a signal flow graph, namely if the cycle products are contained in the Jacobson radical. We show how to construct the smallest ring over which a partially known interconnected system must be reducible. Examples illustrate the application of these results to the study of stability, well-posedness, and asymptotic behavior.