๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Topology and the solution of linear systems

โœ Scribed by Robert B. Ash

Publisher
Elsevier Science
Year
1959
Tongue
English
Weight
521 KB
Volume
268
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

The concepts of linear graph theory are applied to the study of feedback systems. Two topological matrices, called the exit and entrance matrices, are defined and the transmission matrix of the system is expressed in terms of these matrices. The properties of these matrices are examined, and a relation between nonsingular submatrices and nontouchlng feedback loops is established. Graph theory and the theory of determinants allow a rigorous proof of Mason's general gain formula. A systematic method, based on the topological formulas derived in the paper, of finding all forward paths and feedback loops without drawing the graph of the feedback system is demonstrated.

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