H∞ and H2 optimal controllers for periodic and multirate systems

Petros G. Voulgaris; Munther A. Dahleh; Lena S. Valavani

doi:10.1016/0005-1098(94)90028-0

H^∞ and H² optimal controllers for periodic and multirate systems

Petros G. Voulgaris, Munther A. Dahleh, Lena S. Valavani

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

Abstract

In this paper we present the solutions to the optimal l² to l² disturbance rejection problem (H^∞) as well as to the LQG (H²) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H^∞ problem is solved using Nehari's theorem whereas in the H² problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.

Original language	English (US)
Pages (from-to)	251-263
Number of pages	13
Journal	Automatica
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/0005-1098(94)90028-0
State	Published - Feb 1994

Keywords

Discrete time systems
lifts
multirate
optimal control
periodic
robust control

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

Online availability

10.1016/0005-1098(94)90028-0

Library availability

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Cite this

@article{a419e1e883584ec5ae48b15ff9991ba7,

title = "H∞ and H2 optimal controllers for periodic and multirate systems",

abstract = "In this paper we present the solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (H2) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H∞ problem is solved using Nehari's theorem whereas in the H2 problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.",

keywords = "Discrete time systems, lifts, multirate, optimal control, periodic, robust control",

author = "Voulgaris, {Petros G.} and Dahleh, {Munther A.} and Valavani, {Lena S.}",

note = "Funding Information: Acknowledgements--The first and third authors were supported by the AFOSR-Elgin A.F.B. under grant F08635-87-K-0031, by the NASA Ames and Langley Research Centers under grant NASA/NAG-2-297 and by a gift from the Boeing Corporation. The second author was supported by the Draper Laboratory grant DC-H-441636 and by NSF grant 9157306-ECS.",

year = "1994",

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doi = "10.1016/0005-1098(94)90028-0",

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T1 - H∞ and H2 optimal controllers for periodic and multirate systems

AU - Voulgaris, Petros G.

AU - Dahleh, Munther A.

AU - Valavani, Lena S.

N1 - Funding Information: Acknowledgements--The first and third authors were supported by the AFOSR-Elgin A.F.B. under grant F08635-87-K-0031, by the NASA Ames and Langley Research Centers under grant NASA/NAG-2-297 and by a gift from the Boeing Corporation. The second author was supported by the Draper Laboratory grant DC-H-441636 and by NSF grant 9157306-ECS.

PY - 1994/2

Y1 - 1994/2

N2 - In this paper we present the solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (H2) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H∞ problem is solved using Nehari's theorem whereas in the H2 problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.

AB - In this paper we present the solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (H2) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H∞ problem is solved using Nehari's theorem whereas in the H2 problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.

KW - Discrete time systems

KW - lifts

KW - multirate

KW - optimal control

KW - periodic

KW - robust control

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