Generalized Mason's rule: A linear fractional transformation perspective

Abstract Mason's rule is an age‐old and well‐known method for finding the input/output relationships from signal flow graphs or their block diagrams, which is useful for mathematically determining the transfer function of a given feedback system. While Mason's rule is often applied intuitively, users may find it difficult to interpret the rule in the context of the system being analyzed. By disconnecting all of the system's feedback loops and then characterizing the system as a collection of open‐loop subsystems, the linear fractional transformation (LFT) two‐port structure can provide a systematic approach for calculating the input/output transfer function of a given feedback system, particularly for complicated systems that are seemingly challenging using Mason's rule. This study therefore develops the generalized Mason's rule (GMR) using the LFT framework. For simple systems, Mason's rule is advantageous; however, the proposed approach is more favorable for complex systems due to its straightforward nature.