The Aymptotic Behavior of the Root-Loci of Multivariable Optimal Regulators

U. Shaked*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The loci of the closed-loop poles of the multivariable, time-invariant, linear optimal regulator are shown to group into the left half-plane part of several Buttenvorth configurations as the weight on the input in the criterion approaches zero. It is proved that these configurations are of even order and that they are always centered at the origin. The number of configurations of any even order, their radii, and the angle of their corresponding asymptotes are expressed in terms of the criterion and the system constant matrices.

Original languageEnglish
Pages (from-to)425-430
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Jul 1978


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