H∞ control of Lur'e systems with sector and slope restricted nonlinearities

Ju H. Park; D. H. Ji; S. C. Won; S. M. Lee; S. J. Choi

doi:10.1016/j.physleta.2009.08.018

H_∞ control of Lur'e systems with sector and slope restricted nonlinearities

Ju H. Park, D. H. Ji, S. C. Won, S. M. Lee, S. J. Choi

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

22 Scopus citations

Abstract

This Letter considers H_∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H_∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.

Original language	English
Pages (from-to)	3734-3740
Number of pages	7
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	373
Issue number	41
DOIs	https://doi.org/10.1016/j.physleta.2009.08.018
State	Published - 5 Oct 2009

Keywords

LMI
Lur'e systems
Sector and slope restricted nonlinearity
Stabilization

Access to Document

10.1016/j.physleta.2009.08.018

Cite this

@article{7843ba0d77e64844a99383d0720902f8,

title = "H∞ control of Lur'e systems with sector and slope restricted nonlinearities",

abstract = "This Letter considers H∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.",

keywords = "LMI, Lur'e systems, Sector and slope restricted nonlinearity, Stabilization",

author = "Park, {Ju H.} and Ji, {D. H.} and Won, {S. C.} and Lee, {S. M.} and Choi, {S. J.}",

year = "2009",

month = oct,

day = "5",

doi = "10.1016/j.physleta.2009.08.018",

language = "English",

volume = "373",

pages = "3734--3740",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier B.V.",

number = "41",

}

TY - JOUR

T1 - H∞ control of Lur'e systems with sector and slope restricted nonlinearities

AU - Park, Ju H.

AU - Ji, D. H.

AU - Won, S. C.

AU - Lee, S. M.

AU - Choi, S. J.

PY - 2009/10/5

Y1 - 2009/10/5

N2 - This Letter considers H∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.

AB - This Letter considers H∞ controller design scheme for Lur'e systems with sector/slope restrictions and external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, a state feedback controller is designed to not only guarantee stability of systems but also reduce the effect of external disturbance to an H∞ norm constraint. The nonlinearities are expressed as convex combinations of sector and slope bounds so that equality constraints are converted into inequality constraints using convex properties of the nonlinear function. Then, the stabilizing feedback gain matrix is derived through LMI formulation. Finally, a numerical example shows the effectiveness of the proposed method.

KW - LMI

KW - Lur'e systems

KW - Sector and slope restricted nonlinearity

KW - Stabilization

UR - http://www.scopus.com/inward/record.url?scp=70149103984&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2009.08.018

DO - 10.1016/j.physleta.2009.08.018

M3 - Article

AN - SCOPUS:70149103984

SN - 0375-9601

VL - 373

SP - 3734

EP - 3740

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 41

ER -

H_∞ control of Lur'e systems with sector and slope restricted nonlinearities

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this