Matrix scaling for large-scale system decomposition

✍ Scribed by John D. Finney; Bonnie S. Heck

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 777 KB
• Volume: 32
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(96)00018-0

✦ Synopsis

Many large-scale systems exhibit the structure of weakly connected components.

In such cases, proper identification of weakly coupled subsystems will add insight into large-scale system behavior, and aid in related tasks such as the design of decentralized control. e-decomposition is a well-known efficient graph-theoretic algorithm for achieving a complete set of nested decompositions of a large-scale system. This paper shows how system matrix scaling can affect these decompositions, and determines that a system is properly scaled for e-decomposition when it is max-balanced, a property associated with weighted directed graphs. Also, it is shown that an existing algorithm for max-balancing can be altered slightly to return the complete set of Edecompositions, thus removing the need for two separate algorithms. Finally, the advantages of max-balancing before decomposition are shown for the application of decentralized control subsystem identification.