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

U. Shaked

doi:10.1109/TAC.1978.1101737

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

U. Shaked^*

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

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 language	English
Pages (from-to)	425-430
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	23
Issue number	3
DOIs	https://doi.org/10.1109/TAC.1978.1101737
State	Published - Jul 1978

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10.1109/TAC.1978.1101737

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AB - 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.

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

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