Loop Reversal Rule in Block Diagram and Signal Flow Graph Manipulation

Abstract

We propose a new rule, loop reversal, in block diagram and signal flow graph manipulation (or transformation) that leads to equivalent block diagrams or signal flow graphs from existing ones. It is known that “algebraic loops” can exist in some systems, where different choices of causality end up with different yet equivalent block diagrams or signal flow graphs, in which some are loop reversed versions of others. However, to the author's knowledge, loop reversal has not been discussed in the context of block diagram or signal flow graph manipulation, and is still missing from textbooks teaching this topic.