Signal flow graphs-Computer-aided system analysis and sensitivity calculations

Abstract

Concepts which promise to extend many fundamental results of network theory to general systems are introduced. The basis for these extensions is the introduction of two matrices, the summing matrix S and the branching matrix B, which completely describe the topology of a signal flow graph. This leads to a formulation of system equations in terms of submatrices of the S- and B-matrices suitable for digital-computer programming. Consequently, many computer-aided circuit analysis and design programs can now be employed for the computer-aided analysis and design of systems representable by signal flow graphs. This formulation also leads to a straightforward algorithm for obtaining the system gain, an alternate to using Mason's gain formula. Furthermore, the power of this formulation, and its strong relation to network theory, is demonstrated by the derivation of a theorem similar to Tellegen's theorem in network theory. The theorem depends only on the topological properties of the summing and branching matrices and not on the functional relationships between the branch