Many large-scale systems exhibit the structure of weakly connected com
ponents, In such cases, proper identification of weakly coupled subsys
tems will add insight into large-scale system behavior, and aid in rel
ated tasks such as the design of decentralized control. epsilon-decomp
osition is a well-known efficient graph-theoretic algorithm for achiev
ing a complete set of nested decompositions of a large-scale system. T
his paper shows how system matrix scaling can affect these decompositi
ons, and determines that a system is properly scaled for epsilon-decom
position 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 epsilo
n-decompositions, thus removing the need for two separate algorithms.
Finally, the advantages of max-balancing before decomposition are show
n for the application of decentralized control subsystem identificatio
n. Copyright (C) 1996 Elsevier Science Ltd.