Output controllability and eigenvalue assignability in single-output linear systems

For a single-output linear time-invariant system, output controllability is shown to be a necessary and sufficient condition for the existence of linear state variable feedback that freely assigns the eigenvalues of the closed-loop system that are observable from the output. An application of this result to the single-output linear servomechanism shows that the ability of such a system to track with zero steady-state error and an arbitrary transient response is equivalent to output controllability of the plant, and is independent of the class of command signals and disturbances.