Robust decentralized H control for interconnected descriptor systems with norm-bounded uncertainties

Ning Chen, Weihua Gui, Guisheng Zhai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This paper considers a robust decentralized Hcontrol problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method.

Original languageEnglish
Pages (from-to)78-88
Number of pages11
JournalAsian Journal of Control
Volume11
Issue number1
DOIs
Publication statusPublished - 2009 Jan
Externally publishedYes

Fingerprint

Controllers
Linear matrix inequalities
Uncertainty
Feedback

Keywords

  • Decentralized H control
  • Homotopy method
  • Interconnected descriptor systems
  • Nonlinear matrix inequality

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Robust decentralized H control for interconnected descriptor systems with norm-bounded uncertainties. / Chen, Ning; Gui, Weihua; Zhai, Guisheng.

In: Asian Journal of Control, Vol. 11, No. 1, 01.2009, p. 78-88.

Research output: Contribution to journalArticle

@article{17190909016141e29aaa5e033f12682c,
title = "Robust decentralized H∞ control for interconnected descriptor systems with norm-bounded uncertainties",
abstract = "This paper considers a robust decentralized H∞control problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H∞ control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method.",
keywords = "Decentralized H control, Homotopy method, Interconnected descriptor systems, Nonlinear matrix inequality",
author = "Ning Chen and Weihua Gui and Guisheng Zhai",
year = "2009",
month = "1",
doi = "10.1002/asjc.83",
language = "English",
volume = "11",
pages = "78--88",
journal = "Asian Journal of Control",
issn = "1561-8625",
publisher = "National Taiwan University (IEEB)",
number = "1",

}

TY - JOUR

T1 - Robust decentralized H∞ control for interconnected descriptor systems with norm-bounded uncertainties

AU - Chen, Ning

AU - Gui, Weihua

AU - Zhai, Guisheng

PY - 2009/1

Y1 - 2009/1

N2 - This paper considers a robust decentralized H∞control problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H∞ control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method.

AB - This paper considers a robust decentralized H∞control problem for interconnected descriptor systems. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Our interest is focused on dynamic output feedback. A sufficient condition for an uncertain interconnected descriptor system to be robustly stabilizable H∞ control with a specified disturbance attenuation level is derived in terms of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal descriptor system is computed by imposing block-diagonal constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is gradually modified from the nominal descriptor system (without uncertainties) to the original system with uncertainties. On each stage, groups of variables are fixed alternately at the iterations to reduce the NMI to linear matrix inequalities (LMIs). An example is given to show the usefulness of this method.

KW - Decentralized H control

KW - Homotopy method

KW - Interconnected descriptor systems

KW - Nonlinear matrix inequality

UR - http://www.scopus.com/inward/record.url?scp=65549100945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65549100945&partnerID=8YFLogxK

U2 - 10.1002/asjc.83

DO - 10.1002/asjc.83

M3 - Article

VL - 11

SP - 78

EP - 88

JO - Asian Journal of Control

JF - Asian Journal of Control

SN - 1561-8625

IS - 1

ER -