Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

Mahdieh S. Sadabadi; Alireza Karimi

doi:10.1109/ACC.2015.7171172

Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

Mahdieh S. Sadabadi, Alireza Karimi^*

^*Corresponding author for this work

EEE - Academic & Research

Ecole Polytechnique Federale de Lausanne (EPFL)

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

Abstract

This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent gain is determined a priori by means of a parameter-dependent state feedback controller. Simulation results and a comparison with recent existing methods demonstrate the effectiveness of the proposed approach.

Original language	English
Title of host publication	ACC 2015
Subtitle of host publication	2015 American Control Conference
Publisher	IEEE
Pages	2882-2887
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7171172
Publication status	Published - 28 Jul 2015
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: 1 Jul 2015 → 3 Jul 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	1/07/15 → 3/07/15

Keywords

Continuous time systems
Linear control systems
Linear systems
Robustness (control systems)
State feedback

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10.1109/ACC.2015.7171172

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title = "Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness",

abstract = "This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent gain is determined a priori by means of a parameter-dependent state feedback controller. Simulation results and a comparison with recent existing methods demonstrate the effectiveness of the proposed approach.",

keywords = "Continuous time systems, Linear control systems, Linear systems, Robustness (control systems), State feedback",

author = "Sadabadi, {Mahdieh S.} and Alireza Karimi",

note = "Publisher Copyright: {\textcopyright} 2015 American Automatic Control Council.; 2015 American Control Conference, ACC 2015 ; Conference date: 01-07-2015 Through 03-07-2015",

year = "2015",

month = jul,

day = "28",

doi = "10.1109/ACC.2015.7171172",

language = "English",

series = "Proceedings of the American Control Conference",

publisher = "IEEE",

pages = "2882--2887",

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Sadabadi, MS & Karimi, A 2015, Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness. in ACC 2015 : 2015 American Control Conference., 7171172, Proceedings of the American Control Conference, vol. 2015-July, IEEE, pp. 2882-2887, 2015 American Control Conference, ACC 2015, Chicago, United States, 1/07/15. https://doi.org/10.1109/ACC.2015.7171172

Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness. / Sadabadi, Mahdieh S.; Karimi, Alireza.
ACC 2015 : 2015 American Control Conference. IEEE, 2015. p. 2882-2887 7171172 (Proceedings of the American Control Conference; Vol. 2015-July).

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

AU - Sadabadi, Mahdieh S.

AU - Karimi, Alireza

PY - 2015/7/28

Y1 - 2015/7/28

N2 - This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent gain is determined a priori by means of a parameter-dependent state feedback controller. Simulation results and a comparison with recent existing methods demonstrate the effectiveness of the proposed approach.

AB - This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent gain is determined a priori by means of a parameter-dependent state feedback controller. Simulation results and a comparison with recent existing methods demonstrate the effectiveness of the proposed approach.

KW - Continuous time systems

KW - Linear control systems

KW - Linear systems

KW - Robustness (control systems)

KW - State feedback

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U2 - 10.1109/ACC.2015.7171172

DO - 10.1109/ACC.2015.7171172

M3 - Conference contribution

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T3 - Proceedings of the American Control Conference

SP - 2882

EP - 2887

BT - ACC 2015

PB - IEEE

T2 - 2015 American Control Conference, ACC 2015

Y2 - 1 July 2015 through 3 July 2015

ER -

Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

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Keywords

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