Necessary and Sufficient Conditions on Negative Imaginariness for Interval SISO Transfer Functions and Their Interconnection

Mei Liu; James Lam; Hong Lin; Xingjian Jing

doi:10.1109/TAC.2019.2957339

Necessary and Sufficient Conditions on Negative Imaginariness for Interval SISO Transfer Functions and Their Interconnection

Mei Liu
, James Lam
, Hong Lin
, Xingjian Jing

Research output: Journal article publication › Journal article › Academic research › peer-review

6 Citations (Scopus)

Abstract

This article is concerned with the study of the negative imaginariness of interval transfer functions. Necessary and sufficient conditions for (strictly) negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on Kharitonov's theorem. Then, certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed. Finally, an example is provided to illustrate the main results of the article.

Original language	English
Article number	8919984
Pages (from-to)	4362-4368
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	65
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2019.2957339
Publication status	Published - Oct 2020

Keywords

Interval systems
Kharitonov's theorem
negative imaginary systems

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

More information

10.1109/TAC.2019.2957339

Cite this

@article{1c7bf464c578465782b5ad8a4bfe2aac,

title = "Necessary and Sufficient Conditions on Negative Imaginariness for Interval SISO Transfer Functions and Their Interconnection",

abstract = "This article is concerned with the study of the negative imaginariness of interval transfer functions. Necessary and sufficient conditions for (strictly) negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on Kharitonov's theorem. Then, certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed. Finally, an example is provided to illustrate the main results of the article. ",

keywords = "Interval systems, Kharitonov's theorem, negative imaginary systems",

author = "Mei Liu and James Lam and Hong Lin and Xingjian Jing",

note = "Funding Information: Manuscript received September 19, 2018; revised March 10, 2019 and November 5, 2019; accepted November 15, 2019. Date of publication December 3, 2019; date of current version September 25, 2020. This work was supported in part by a general research fund of Hong Kong RGC Ref. 15206717 and in part by Tianjin University under Start-Up Grant 0701321009. Recommended by Associate Editor A. Lanzon. (Corresponding author: James Lam.) M. Liu is with the Department of Automation, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China, and also with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong (e-mail: [email protected]). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2020",

month = oct,

doi = "10.1109/TAC.2019.2957339",

language = "English",

volume = "65",

pages = "4362--4368",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "IEEE",

number = "10",

}

TY - JOUR

T1 - Necessary and Sufficient Conditions on Negative Imaginariness for Interval SISO Transfer Functions and Their Interconnection

AU - Liu, Mei

AU - Lam, James

AU - Lin, Hong

AU - Jing, Xingjian

N1 - Funding Information: Manuscript received September 19, 2018; revised March 10, 2019 and November 5, 2019; accepted November 15, 2019. Date of publication December 3, 2019; date of current version September 25, 2020. This work was supported in part by a general research fund of Hong Kong RGC Ref. 15206717 and in part by Tianjin University under Start-Up Grant 0701321009. Recommended by Associate Editor A. Lanzon. (Corresponding author: James Lam.) M. Liu is with the Department of Automation, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China, and also with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong (e-mail: [email protected]). Publisher Copyright: © 1963-2012 IEEE.

PY - 2020/10

Y1 - 2020/10

N2 - This article is concerned with the study of the negative imaginariness of interval transfer functions. Necessary and sufficient conditions for (strictly) negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on Kharitonov's theorem. Then, certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed. Finally, an example is provided to illustrate the main results of the article.

AB - This article is concerned with the study of the negative imaginariness of interval transfer functions. Necessary and sufficient conditions for (strictly) negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on Kharitonov's theorem. Then, certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed. Finally, an example is provided to illustrate the main results of the article.

KW - Interval systems

KW - Kharitonov's theorem

KW - negative imaginary systems

UR - https://www.scopus.com/pages/publications/85089549128

U2 - 10.1109/TAC.2019.2957339

DO - 10.1109/TAC.2019.2957339

M3 - Journal article

AN - SCOPUS:85089549128

SN - 0018-9286

VL - 65

SP - 4362

EP - 4368

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

M1 - 8919984

ER -

Necessary and Sufficient Conditions on Negative Imaginariness for Interval SISO Transfer Functions and Their Interconnection

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this