MATRIX SCALING FOR LARGE-SCALE SYSTEM DECOMPOSITION

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.