Single Diophantine equation polynomial discrete-time H2 and H∞ controller computation

Haipeng Zhao; Joseph Bentsman

doi:10.1016/S1474-6670(17)35713-0

Single Diophantine equation polynomial discrete-time H₂ and H_∞ controller computation

Research output: Contribution to journal › Conference article › peer-review

Abstract

In (Zhao and Bentsman, 2002} it has been shown that for most singlein put-single-output linear discrete-time systems in polynomial format, a sequential solution of a Diophantine equation and an algebraic equation is, in theory, sufficient to calculate the corresponding H₂ and H_∞ controllers, Based on the results of (Zhao and Bentsman, 2002), the present work gives procedures for determining the sufficiency of a single Diophantine equation for controller calculation and for the actual calculation of the optimal controllers. Controller computations for nonminimum phase unstable plants have been carried out with relative ease.

Original language	English (US)
Pages (from-to)	499-504
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	36
Issue number	11
DOIs	https://doi.org/10.1016/S1474-6670(17)35713-0
State	Published - 2003
Event	4th IFAC Symposium on Robust Control Design, ROCOND 2003 - Milan, Italy Duration: Jun 25 2003 → Jun 27 2003

Keywords

Discrete-time systems
H optimal control
Polynomial methods
Quadratic optimal regulators
Robust control

ASJC Scopus subject areas

Control and Systems Engineering

Online availability

10.1016/S1474-6670(17)35713-0

Library availability

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Cite this

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title = "Single Diophantine equation polynomial discrete-time H2 and H∞ controller computation",

abstract = "In (Zhao and Bentsman, 2002} it has been shown that for most singlein put-single-output linear discrete-time systems in polynomial format, a sequential solution of a Diophantine equation and an algebraic equation is, in theory, sufficient to calculate the corresponding H2 and H∞ controllers, Based on the results of (Zhao and Bentsman, 2002), the present work gives procedures for determining the sufficiency of a single Diophantine equation for controller calculation and for the actual calculation of the optimal controllers. Controller computations for nonminimum phase unstable plants have been carried out with relative ease.",

keywords = "Discrete-time systems, H optimal control, Polynomial methods, Quadratic optimal regulators, Robust control",

author = "Haipeng Zhao and Joseph Bentsman",

note = "Publisher Copyright: {\textcopyright} 2003 1FAC.; 4th IFAC Symposium on Robust Control Design, ROCOND 2003 ; Conference date: 25-06-2003 Through 27-06-2003",

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T1 - Single Diophantine equation polynomial discrete-time H2 and H∞ controller computation

AU - Zhao, Haipeng

AU - Bentsman, Joseph

PY - 2003

Y1 - 2003

N2 - In (Zhao and Bentsman, 2002} it has been shown that for most singlein put-single-output linear discrete-time systems in polynomial format, a sequential solution of a Diophantine equation and an algebraic equation is, in theory, sufficient to calculate the corresponding H2 and H∞ controllers, Based on the results of (Zhao and Bentsman, 2002), the present work gives procedures for determining the sufficiency of a single Diophantine equation for controller calculation and for the actual calculation of the optimal controllers. Controller computations for nonminimum phase unstable plants have been carried out with relative ease.

AB - In (Zhao and Bentsman, 2002} it has been shown that for most singlein put-single-output linear discrete-time systems in polynomial format, a sequential solution of a Diophantine equation and an algebraic equation is, in theory, sufficient to calculate the corresponding H2 and H∞ controllers, Based on the results of (Zhao and Bentsman, 2002), the present work gives procedures for determining the sufficiency of a single Diophantine equation for controller calculation and for the actual calculation of the optimal controllers. Controller computations for nonminimum phase unstable plants have been carried out with relative ease.

KW - Discrete-time systems

KW - H optimal control

KW - Polynomial methods

KW - Quadratic optimal regulators

KW - Robust control

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