The parametrization of all controllers that achieve output regulation and tracking

The authors consider frequency-domain conditions for feedback compensators that achieve output regulation and tracking in the presence of persistent set points inputs. Using a standard plant approach it is shown that the property of internal stability must be relaxed to what is defined as tracking stability. A characterization of all controllers is formulated in terms of an extended plant description. The formulation provides a framework for compensator design when both regulator and tracking objectives have to be satisfied. It allows application of control design methods like H₂ and H_∞ optimal control to consider tradeoffs between tracking properties and other design objectives