An optimal controller reduction by covariance equivalent realizations

Based upon the theory of covariance equivalent realizations [1], this note presents a technique to obtain reduced-order controllers via an optimal projection of full-order LQG-controllers. This projection is optimal in the sense that it is a weighted least square approximation to a covariance equivalent projection of the full-order optimal closed-loop system. The technique, which is capable of extracting optimal, minimal LQG-controllers whenever they exist, is also shown to yield controllers that are equivalent to those obtained by component cost analysis [12].