# Optimal pole allocation and weighting matrix selection

Tsu Tian Lee, Jyh-Chin Juang

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The Levy-Hadamard's theorem and Bendixson's theorem are applied to derived algebraic relations which will set bounds on the real and imaginary parts of the eigenvalues of the closed-loop matrix. It is shown that the required feedback matrix can be found very simply. Further, the inverse problem of optimal control, which characterizes the cost function based on the given feedback matrix, is considered. Gutman and Jury's (1981) result is used to derive some algebraic relations which cluster the feedback system poles inside a second-order curve in the complex frequency s-plane. It is also shown that once these relations are obtained, a proposed algorithm can be performed readily to determine the quadratic performance index of linear optimal control problems.

Original language English 325-336 12 International Journal of Systems Science 17 2 https://doi.org/10.1080/00207728608926807 Published - 1986 Jan 1

### Fingerprint

Weighting
Pole
Poles
Feedback
Linear Control
Feedback Systems
Performance Index
Inverse problems
Theorem
Cost functions
Closed-loop
Cost Function
Optimal Control Problem
Inverse Problem
Optimal Control
Eigenvalue
Curve

### All Science Journal Classification (ASJC) codes

• Control and Systems Engineering
• Theoretical Computer Science
• Computer Science Applications

### Cite this

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In: International Journal of Systems Science, Vol. 17, No. 2, 01.01.1986, p. 325-336.

Research output: Contribution to journalArticle

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AU - Juang, Jyh-Chin

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Y1 - 1986/1/1

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AB - The Levy-Hadamard's theorem and Bendixson's theorem are applied to derived algebraic relations which will set bounds on the real and imaginary parts of the eigenvalues of the closed-loop matrix. It is shown that the required feedback matrix can be found very simply. Further, the inverse problem of optimal control, which characterizes the cost function based on the given feedback matrix, is considered. Gutman and Jury's (1981) result is used to derive some algebraic relations which cluster the feedback system poles inside a second-order curve in the complex frequency s-plane. It is also shown that once these relations are obtained, a proposed algorithm can be performed readily to determine the quadratic performance index of linear optimal control problems.

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