Feedback system design: The fractional representation approach to analysis and synthesis

The problem of designing a feedback system with prescribed properties is attacked via a fractional representation approach to feedback system analysis and synthesis. To this end we let denote a ring of operators with the prescribed properties and model a given plant as the ratio of two operators in . This, in turn, leads to a simplified test to determine whether or not a feedback system in which that plant is embedded has the prescribed properties and a complete characterization of those compensators which will "place" the feedback system in . The theory is formulated axiomatically to permit its application in a wide variety of system design problems and is extremely elementary in nature requiring no more than addition, multiplication, subtraction, and inversion for its derivation even in the most general settings.