On a property of compensators designed by the separation principle

The transfer function of a full-order compensator for a single-input, single-output (SISO) linear system designed by the separation principle is uniquely determined by the locations of the poles of the closed-loop system and its gain. Hence, the poles of the observer and of the full-state feedback design can be interchanged without altering the transfer function of the compensator. A state space derivation of this property is presented.<>