Vector L2-gain and a small gain theorem for switched systems

Jun Zhao; David J.hill

doi:10.3182/20050703-6-cz-1902.00302

Vector L₂-gain and a small gain theorem for switched systems

Jun Zhao
, David J.hill

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

2 Citations (Scopus)

Abstract

A concept of vector L₂-gain is presented for switched systems. Each subsystem is allowed to have individual input-outputL₂-gain during any time interval when the subsystem is activated. Stability is derived from this vector L₂- gain for certain classes of control including output feedback. A small gain theorem for switched systems with vector L ₂-gain is established which provides a tool for analyzing the behavior of feedback interconnected switched systems. The small gain condition is given in terms of the L₂-gain of the coupled activated subsystems.

Original language	English
Title of host publication	Proceedings of the 16th IFAC World Congress, IFAC 2005
Publisher	Elsevier - International Federation of Automatic Control (IFAC)
Pages	103-108
Number of pages	6
ISBN (Print)	008045108X, 9780080451084
DOIs	https://doi.org/10.3182/20050703-6-cz-1902.00302
Publication status	Published - 2005
Externally published	Yes
Event	International Federation of Automatic Control World Congress 2005 - Prague Congress Center, Prague, Czechia Duration: 3 Jul 2005 → 8 Jul 2005 Conference number: 16th

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	16
ISSN (Print)	1474-6670

Conference

Conference	International Federation of Automatic Control World Congress 2005
Abbreviated title	IFAC 2005
Country/Territory	Czechia
City	Prague
Period	3/07/05 → 8/07/05

Keywords

Feedback interconnection
Stability
Switched systems

Access to Document

10.3182/20050703-6-cz-1902.00302

Cite this

@inproceedings{673f0e7ce1d048c394b87c7da5f29e46,

title = "Vector L2-gain and a small gain theorem for switched systems",

abstract = "A concept of vector L2-gain is presented for switched systems. Each subsystem is allowed to have individual input-outputL2-gain during any time interval when the subsystem is activated. Stability is derived from this vector L2- gain for certain classes of control including output feedback. A small gain theorem for switched systems with vector L 2-gain is established which provides a tool for analyzing the behavior of feedback interconnected switched systems. The small gain condition is given in terms of the L2-gain of the coupled activated subsystems.",

keywords = "Feedback interconnection, Stability, Switched systems",

author = "Jun Zhao and David J.hill",

note = "Funding Information: 1 This work was supported by the Hong Kong Research Grants Council under Project No. CityU 1232/02E, City University of Hong Hong under Project 9380026 and NSF of China under Grant No.60274009; International Federation of Automatic Control World Congress 2005, IFAC 2005 ; Conference date: 03-07-2005 Through 08-07-2005",

year = "2005",

doi = "10.3182/20050703-6-cz-1902.00302",

language = "English",

isbn = "008045108X",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "Elsevier - International Federation of Automatic Control (IFAC)",

pages = "103--108",

booktitle = "Proceedings of the 16th IFAC World Congress, IFAC 2005",

}

Zhao, J & J.hill, D 2005, Vector L₂-gain and a small gain theorem for switched systems. in Proceedings of the 16th IFAC World Congress, IFAC 2005. IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 16, Elsevier - International Federation of Automatic Control (IFAC), pp. 103-108, International Federation of Automatic Control World Congress 2005, Prague, Czechia, 3/07/05. https://doi.org/10.3182/20050703-6-cz-1902.00302

Vector L₂-gain and a small gain theorem for switched systems. / Zhao, Jun; J.hill, David.
Proceedings of the 16th IFAC World Congress, IFAC 2005. Elsevier - International Federation of Automatic Control (IFAC), 2005. p. 103-108 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 16).

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

TY - GEN

T1 - Vector L2-gain and a small gain theorem for switched systems

AU - Zhao, Jun

AU - J.hill, David

N1 - Conference code: 16th

PY - 2005

Y1 - 2005

N2 - A concept of vector L2-gain is presented for switched systems. Each subsystem is allowed to have individual input-outputL2-gain during any time interval when the subsystem is activated. Stability is derived from this vector L2- gain for certain classes of control including output feedback. A small gain theorem for switched systems with vector L 2-gain is established which provides a tool for analyzing the behavior of feedback interconnected switched systems. The small gain condition is given in terms of the L2-gain of the coupled activated subsystems.

AB - A concept of vector L2-gain is presented for switched systems. Each subsystem is allowed to have individual input-outputL2-gain during any time interval when the subsystem is activated. Stability is derived from this vector L2- gain for certain classes of control including output feedback. A small gain theorem for switched systems with vector L 2-gain is established which provides a tool for analyzing the behavior of feedback interconnected switched systems. The small gain condition is given in terms of the L2-gain of the coupled activated subsystems.

KW - Feedback interconnection

KW - Stability

KW - Switched systems

UR - https://www.scopus.com/pages/publications/79960733550

U2 - 10.3182/20050703-6-cz-1902.00302

DO - 10.3182/20050703-6-cz-1902.00302

M3 - Conference Paper

AN - SCOPUS:79960733550

SN - 008045108X

SN - 9780080451084

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 103

EP - 108

BT - Proceedings of the 16th IFAC World Congress, IFAC 2005

PB - Elsevier - International Federation of Automatic Control (IFAC)

T2 - International Federation of Automatic Control World Congress 2005

Y2 - 3 July 2005 through 8 July 2005

ER -