A digital procedure for finding all directed subgraphs of a signal flow graph

The algebra of flow graphs is well defined and several techniques are available for obtaining input-output relations. A brief review is presented with the addition of the application to sampled data systems. However, all of the techniques for obtaining input-output relations depend upon the users ability to identify all subgraphs within his system flow graph. Several papers have been presented concerning error free identification of these loops and paths, however, the techniques involved are usually laborious and lengthy. Through the use of the connection matrix approach of Mr. C. V. Ramamoorthy a digitial computer program is developed that finds all loops and paths that exist within a flow graph. This research was restricted to only continuous variable systems, however, techniques are suggested for handling the hybrid case, containing discrete as well as continuous variables. Several examples are preseneted to demonstrate the capability of the program. Suggestions are also made for handling multi-input-output problems.