The all-pass property of optimal open-loop tracking systems

The structure of the optimal open-loop linear model-following system is investigated. It is shown that if the given plant is asymptotically stable but has zeros in the right half-plane, the stable optimal system contains an all-pass network whose transference possesses unity, singular values on the imaginary axis. In the special case of optimal tracking, it is shown that the resulting optimal transfer function matrix of the system is equal to the all-pass transfer function matrix which is normalized to be the identity matrix at the zero frequency.