On the Class of All Stabilizing Regulators

The `internal model principle' for linear multivariable regulators tells us necessary and sufficient conditions for achieving stabilizing controllers which achieve structurally stable output regulation for classes of deterministic exogenous reference and disturbance signals. In the absence of structural stability considerations, Antoulas has characterized the entire class of stabilizing regulators in the time-invariant case, building on the Kucera/Youla parametrization techniques. This paper gives an alternative characterization of the class of stabilizing regulators which is convenient to achieve on-line or off-line H
²
/H
^∞
optimization for performance and robustness. The characterization exploits distubance signal reconstruction, and nulling filters. The theory allows a re-interpretation of the necessary and sufficient conditions for regulation. Also novel connections between structurally stable regulation and the internal model principle are exposed.