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On the Global Properties of Interconnected Systems

TitleOn the Global Properties of Interconnected Systems
Publication TypeJournal Article
Year of Publication1995
AuthorsPliam JO, Lee BE
Keywordsalgebraic systems theory, signal flow graphs, systems over rings
AbstractInterconnected 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.