The All-Pass Property of Optimal Open-Loop Tracking Systems

U. Shaked*, U. Shaked*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)465-467
Number of pages3
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - May 1984


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