A UNIFICATION OF ANALYTICAL EXPRESSIONS FOR CONTROL PERFORMANCE LIMITATIONS VIA RECIPROCAL TRANSFORM

This paper formally introduces a concept named “Reciprocal Transform” for unifying analytical expressions on control performance limits achievable by feedback for continuous-time systems. The transform swaps the role of poles and zeros and takes the reciprocal values. We first show its several properties and the state-space form. We then review Bode integral type relations and investigate performance limits for H2 tracking and regulation problems and H∞ control problems including loop shaping design. The investigations confirm the role of reciprocal transform in control performance limitations.