Decentralized H∞ controller design for descriptor systems

Guisheng Zhai; Naoki Koyama; Masaharu Yoshida

doi:10.1016/S1474-6670(17)31628-2

Decentralized H∞ controller design for descriptor systems

Guisheng Zhai, Naoki Koyama, Masaharu Yoshida

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

1 Citation (Scopus)

Abstract

This paper considers a decentralized H∞, control problem for multichannel linear time-invariant (LTI) descriptor systems. Our interest is to design a low order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix and a matrix related to the descriptor matrix. There is no globally effective method for solving general BMIs. In this paper, under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), we propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.

Original language	English
Pages (from-to)	303-308
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	37
Issue number	11
DOIs	https://doi.org/10.1016/S1474-6670(17)31628-2
Publication status	Published - 2004
Externally published	Yes
Event	10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, LSS 2004 - Osaka, Japan Duration: 2004 Jul 26 → 2004 Jul 28

Keywords

Bilinear matrix inequality (BMI)
Decentralized H∞ control
Linear matrix inequality (LMI)
Low order
Multi-channel LTI descriptor system

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/S1474-6670(17)31628-2

Cite this

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title = "Decentralized H∞ controller design for descriptor systems",

abstract = "This paper considers a decentralized H∞, control problem for multichannel linear time-invariant (LTI) descriptor systems. Our interest is to design a low order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix and a matrix related to the descriptor matrix. There is no globally effective method for solving general BMIs. In this paper, under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), we propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.",

keywords = "Bilinear matrix inequality (BMI), Decentralized H∞ control, Linear matrix inequality (LMI), Low order, Multi-channel LTI descriptor system",

author = "Guisheng Zhai and Naoki Koyama and Masaharu Yoshida",

note = "Funding Information: The authors would like to thank Professor Masao IKEDA of Osaka University and Professor Noboru SEBE of Kyushu Institute of Technology, for their valuable discussions that greatly contributed to this paper. Publisher Copyright: {\textcopyright} 2004 IFAC.; 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, LSS 2004 ; Conference date: 26-07-2004 Through 28-07-2004",

year = "2004",

doi = "10.1016/S1474-6670(17)31628-2",

language = "English",

volume = "37",

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TY - JOUR

T1 - Decentralized H∞ controller design for descriptor systems

AU - Zhai, Guisheng

AU - Koyama, Naoki

AU - Yoshida, Masaharu

N1 - Funding Information: The authors would like to thank Professor Masao IKEDA of Osaka University and Professor Noboru SEBE of Kyushu Institute of Technology, for their valuable discussions that greatly contributed to this paper. Publisher Copyright: © 2004 IFAC.

PY - 2004

Y1 - 2004

N2 - This paper considers a decentralized H∞, control problem for multichannel linear time-invariant (LTI) descriptor systems. Our interest is to design a low order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix and a matrix related to the descriptor matrix. There is no globally effective method for solving general BMIs. In this paper, under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), we propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.

AB - This paper considers a decentralized H∞, control problem for multichannel linear time-invariant (LTI) descriptor systems. Our interest is to design a low order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix and a matrix related to the descriptor matrix. There is no globally effective method for solving general BMIs. In this paper, under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), we propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.

KW - Bilinear matrix inequality (BMI)

KW - Decentralized H∞ control

KW - Linear matrix inequality (LMI)

KW - Low order

KW - Multi-channel LTI descriptor system

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U2 - 10.1016/S1474-6670(17)31628-2

DO - 10.1016/S1474-6670(17)31628-2

M3 - Conference article

AN - SCOPUS:85064449655

SN - 1474-6670

VL - 37

SP - 303

EP - 308

JO - IFAC Proceedings Volumes (IFAC-PapersOnline)

JF - IFAC Proceedings Volumes (IFAC-PapersOnline)

IS - 11

T2 - 10th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory and Applications, LSS 2004

Y2 - 26 July 2004 through 28 July 2004

ER -

Decentralized H∞ controller design for descriptor systems

Abstract

Keywords

ASJC Scopus subject areas

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