Invariants of optimal minimal-order observer-based compensators

The relations characterizing the optimal minimal-order observer-based compensators for a linear time-invariant multivariable system with a random initial state (or, equivalently, known initial state and white plant-driving noise) have been reported by Miller [1]. In this note we establish in general that the plant transfer function uniquely determines the optimal compensator transfer function, and that this characterizes precisely the degrees of freedom in the compensator design; computational implications of this result are indicated.